CONTRIBUTION AND CONVEYANCE AGREEMENT by and among

Exhibit 10.35

CONTRIBUTION AND CONVEYANCE AGREEMENT

by and among

ENERGY TRANSFER PARTNERS, L.P.

AND

ENERGY TRANSFER EQUITY, L.P.

(Class G Units)

Dated November 1, 2006

CONTRIBUTION AND CONVEYANCE AGREEMENT

THIS CONTRIBUTION AND CONVEYANCE AGREEMENT, dated November 1, 2006 (this “Agreement”), is made by Energy Transfer Partners, L.P., a limited partnership formed under the laws of the State of Delaware ( “ETP” or the “Partnership”), on the one hand, and Energy Transfer Equity, L.P., a limited partnership formed under the laws of the State of Delaware ( “ETE”), on the other hand.

WHEREAS, ETP desires to issue to ETE, in exchange for a contribution by ETE of cash, limited partner interests of the Partnership, consisting of Class G Units (the “Class G Units”), having the characteristics set forth in Amendment No. 10 to the Amended and Restated Agreement of Limited Partnership of the Partnership (“Amendment No. 10”), a copy of which is attached hereto as Exhibit A.

NOW, THEREFORE, in consideration of the mutual covenants and agreements set forth herein and for good and valuable consideration, the receipt and sufficiency of which are hereby acknowledged, ETP and ETE hereby agree as follows:

ARTICLE I.

DEFINITIONS

Section 1.01 Definitions. As used in this Agreement, and unless the context requires a different meaning, the following terms have the meanings indicated:

“Cash Contribution” shall have the meaning specified in Section 2.01.

“CCE Purchase Agreement” means the Purchase and Sale Agreement, dated as of September 14, 2006, among the Partnership and the Class B Members of CCE Holdings, LLC.

“Class G Units” shall have the meaning specified in Section 2.02.

“Closing” shall have the meaning specified in Section 2.03.

“Closing Date” shall have the meaning specified in Section 2.03.

“Common Units” means common units representing limited partnership interests of ETP.

“Commission” means the United States Securities and Exchange Commission.

“ETP” has the meaning set forth in the introductory paragraph.

“Exchange Act” means the Securities Exchange Act of 1934, as amended.

“Governmental Authority” means, with respect to a particular Person, the country, state, county, city and political subdivisions in which such Person, such Person’s Subsidiaries or such Person’s Property is located or which exercises valid jurisdiction over any such Person or such Person’s Property, and any court, agency, department, commission, board, bureau or

instrumentality of any of them and any monetary authority which exercises valid jurisdiction over any such Person or such Person’s Property.

“Material Adverse Effect” means any event or condition that has had or could reasonably be expected to (i) have a material adverse effect on the financial condition, results of operations, business or prospects of such party, (ii) result in termination of the CCE Purchase Agreement, (iii) result in a breach or violation of any representation, warranty, covenant or condition contained in the CCE Purchase Agreement as a result of which a party to the CCE Purchase Agreement has, or with notice, the lapse of time or both, is likely to have, the right to terminate the CCE Purchase Agreement or (iv) impair or affect adversely such party’s ability to perform its obligations under the Agreement or impair or delay completion of the transactions contemplated hereby or by the CCE Purchase Agreement.

“Person” means any individual, corporation, company, voluntary association, partnership, joint venture, trust, limited liability company, unincorporated organization or government or any agency, instrumentality or political subdivision thereof, or any other form of entity.

“Property” means any interest in any kind of property or asset, whether real, personal or mixed, or tangible or intangible.

“Securities Act” means the Securities Act of 1933, as amended.

“Subsidiary” means, as to any Person, any corporation or other entity of which: (i) such Person or a Subsidiary of such Person is a general partner or manager; or (ii) at least a majority of the outstanding equity interest having by the terms thereof ordinary voting power to elect a majority of the board of directors or similar governing body of such corporation or other entity (irrespective of whether or not at the time any equity interest of any other class or classes of such corporation or other entity shall have or might have voting power by reason of the happening of any contingency) is at the time directly or indirectly owned or controlled by such Person or one or more of its Subsidiaries.

“Transwestern” means Transwestern Pipeline Company, LLC, a Delaware limited liability company.

ARTICLE II.

CONTRIBUTIONS, ACKNOWLEDGMENTS AND DISTRIBUTIONS

Section 2.01 Contribution of Cash to ETP. Subject to the terms and conditions hereof, ETE hereby agrees to contribute, grant, bargain, convey, assign, transfer, set over and deliver to ETP, its successors and assigns, cash in the amount of $1.2 billion (“Cash Contribution”) as a contribution to the capital of ETP and ETP hereby agrees to accept such Cash Contribution as a contribution to the capital of ETP.

Section 2.02 Issuance of Class G Units. Subject to the terms and conditions of this Agreement, ETP agrees to issue to ETE, 26,086,957 Class G Units the “Class G Units”) in exchange for the contribution of the Cash Contribution by ETE and ETE hereby agrees to accept the Class G Units in exchange for its capital contribution of the Cash Contribution to ETP. The issuance of the Class G Units contemplated hereby will not be registered with the Securities and

2

Exchange Commission (the “Commission”) under the Securities Act of 1933, as amended (the “Act”) and the certificates representing such Class G Units shall be issued bearing a restrictive legend thereon in the form of Exhibit B attached hereto.

Section 2.03 Closing and Delivery of Class G Units.

(a) Subject to the terms and conditions hereof, the closing of the transactions constituting the issuance of the Class G Units and the contribution of the Cash Contribution (the “Closing”) shall take place at the offices of Vinson & Elkins, L.L.P., counsel to ETE, 1001 Fannin Street, Houston, Texas, at 3:00 p.m. Central Time on November 1, 2006, or such other date, place and time as ETP and ETE may agree (the “Closing Date”).

(b) The Class G Units to be issued to ETE under this Agreement shall be delivered by or on behalf of ETP to ETE at the Closing in certificated form.

(c) The Cash Contribution shall be by payment by wire transfer in immediately available funds to such bank account of ETP designated by ETP in writing no later than the Business Day immediately preceding the Closing Date. “Business Day” means any day other than (a) a Saturday, Sunday or legal holiday in New York City, or (b) a day on which the commercial banks in New York City are authorized or required by law or executive order to close.

Section 2.04 Conditions to the Closing.

(a) ETE’s Conditions. The obligations of ETE to consummate the purchase of its Class G Units shall be subject to the satisfaction on or prior to the Closing Date of the following conditions (any or all of which may be waived by ETE in writing, in whole or in part, to the extent permitted by applicable Law):

(i) the representations and warranties of ETP contained in this Agreement shall be true and correct in all material respects both when made and at and as of the Closing Date, as if made at and as of such time (except to the extent expressly made as of an earlier date, in which case as of such date), and ETE shall have received an officer’s certificate signed on behalf of ETP to such effect;

(ii) the execution and delivery by ETP of a Registration Rights Agreement in the form attached hereto as Exhibit C; and

(iii) all conditions to closing under the CCE Purchase Agreement have been satisfied or waived other than the delivery of closing items pursuant to Section 2.4 of the CCE Purchase Agreement;

(b) ETP’s Conditions. The obligation of ETP to consummate the issuance of the Class G Units to ETE shall be subject to the satisfaction on or prior to the Closing Date of the following conditions (which may be waived by ETP in writing, in whole or in part, to the extent permitted by applicable Law):

3

(i) the representations and warranties of ETE contained in this Agreement shall be true and correct in all material respects both when made and at and as of the Closing Date, as if made at and as of such time (except to the extent expressly made as of an earlier date, in which case as of such date), and ETP shall have received an officer’s certificate from ETE signed on behalf of ETE to such effect;

(ii) all conditions to closing under the CCE Purchase Agreement have been satisfied or waived other than the delivery of closing items pursuant to Section 2.4 of the CCE Purchase Agreement;

(iii) payment to ETP of the amount of the Cash Contribution in exchange for the Class G Units; and

(iv) the execution and delivery by ETE of the Registration Rights Agreement.

ARTICLE III.

REPRESENTATIONS AND WARRANTIES OF ETP

ETP represents and warrants to ETE as follows:

Section 3.01 Existence. ETP (i) is a limited partnership duly organized, legally existing and in good standing under the laws of the State of Delaware and (ii) has all requisite power and authority, and has all governmental licenses, authorizations, consents and approvals necessary, to own, lease, use and operate its Properties and carry on its business as its business is now being conducted, except where the failure to obtain such licenses, authorizations, consents and approvals would not be reasonably likely to have a Material Adverse Effect.

Section 3.02 Valid Issuance of Class G Units. ETP has taken all necessary action to approve and adopt Amendment No. 10 as an amendment to the Amended and Restated Agreement of Limited Partnership of ETP, as amended as of the date of this Agreement (the “Partnership Agreement”) and no approval of the limited partners of ETP is necessary for the approval and adoption of Amendment No. 10. Amendment No. 10 has been duly executed, delivered and adopted by ETP as an amendment to the Partnership Agreement. ETE, when such Class G Units are delivered as provided in this Agreement, will be entitled to the rights of a unitholder of limited partner interests of ETP as conferred by the Partnership Agreement, as amended by Amendment No. 10, and applicable law. The issuance of the Class G Units and the limited partner interests represented thereby have been duly authorized by ETP and, when issued and delivered to ETE against payment therefor in accordance with the terms of this Agreement, will be validly issued, fully paid (to the extent required under the Partnership Agreement) and nonassessable (except as such nonassessability may be affected by such matters described under the caption “The Partnership Agreement—Limited Liability” in ETP’s Registration Statement on Form S-3 (File No. 333-133174).

Section 3.03 Authority. ETP has all necessary power and authority to execute, deliver and perform its obligations under this Agreement; and the execution, delivery and performance by ETP of this Agreement has been duly authorized by all necessary action on its part; and this Agreement constitutes the legal, valid and binding obligations of ETP, enforceable in accordance

4

with its terms, except as such enforceability may be limited by bankruptcy, insolvency, fraudulent transfer and similar laws affecting creditors’ rights generally or by general principles of equity. No approval from the equity owners of ETP is required in connection with the transactions contemplated by this Agreement.

Section 3.04 Approvals. No authorization, consent, approval, waiver, license, qualification or written exemption from, nor any filing, declaration, qualification or registration with, any Governmental Authority or any other Person (each, a “Consent”) is required for the issuance and delivery of the Class G Units being sold by ETP to ETE or in connection with the execution, delivery or performance by ETP of this Agreement other than Consents that have been obtained.

Section 3.05 No Breach. The execution and delivery of this Agreement, the compliance by ETP with all the provisions of, and the performance by ETP of its obligations under, this Agreement, and the consummation of the transactions contemplated in this Agreement will not conflict with or result in a breach or violation of any of the terms or provisions of, or constitute a default under, (i) the constitutive documents of ETP, (ii) any instrument, contract or other agreement to which ETP is a party or by which ETP is bound or to which any of its Properties or assets may be bound or subject, in each case, the breach or violation of which or default under which would be reasonably expected to have a Material Adverse Effect on the ability of ETP to comply with its obligations hereunder, or (iii) any law or statute or any order, rule or regulation of any Governmental Authority.

Section 3.06 Title. Such Class G Units are not subject to any conflicting sale, transfer, assignment, or any agreement (other than this Agreement) to assign, convey, or transfer, in whole or in part, any of such Class G Units, and upon consummation of such Purchase, ETE will receive good and marketable title to such Class G Units, free and clear of any encumbrance, liens, claims, charges, security interests, or other interests of others, except to the extent of any encumbrance, lien, claim, charge, security interest or other interest created by ETE.

Section 3.07 Legal Proceedings. There are no legal or governmental proceedings pending to which ETP is a party or of which any property of ETP is the subject that, if determined adversely to ETP, would individually or in the aggregate have a Material Adverse Effect on ETP, and, to the best of ETP’s knowledge, no such proceedings are threatened or contemplated by any such Governmental Authority or threatened by others.

Section 3.08 ETP Commission Documents. ETP has filed with the Commission all forms, registration statements, reports, schedules and statements required to be filed by it under the Exchange Act or the Securities Act within the 18 months prior to the date of this Agreement (all such documents, collectively “ETP Commission Documents”). ETP Commission Documents, including, without limitation, any audited or unaudited financial statements and any notes thereto or schedules included therein, at the time filed (in the case of registration statements, solely on the dates of effectiveness) (except to the extent corrected by a subsequently filed ETP Commission Document filed prior to the date hereof) (a) complied as to form in all material respects with applicable accounting requirements and with the published rules and regulations of the Commission with respect thereto, (b) were prepared in accordance with generally accepted accounting principles applied on a consistent basis during the periods

5

involved (except as may be indicated in the notes thereto or, in the case of unaudited statements, as permitted by the applicable rules and regulations of the Commission), and (c) fairly present (subject in the case of unaudited statements to normal, recurring and year-end audit adjustments) in all material respects the consolidated financial position and status of the business of ETP as of the dates thereof and the consolidated results of its operations and cash flows for the periods then ended.

Section 3.09 No Material Adverse Changes. Except as disclosed in the documents filed by ETP under the Exchange Act, since the date of ETP’s most recent Form 8-K (to the extent it contains financial results and balance sheet information) or Form 10-Q filing with the Commission, ETP and its subsidiaries have conducted their respective businesses in the ordinary course, consistent with past practice, and there has been no change, event, occurrence, fact, circumstance or condition that has had or would be reasonably likely to have a Material Adverse Effect on the assets, liabilities, financial condition, business, operations or affairs of ETP and its subsidiaries, taken as a whole.

Section 3.10 CCE Purchase Agreement. The CCE Purchase Agreement is in full force and effect and, to the best knowledge of ETP, no event or circumstance has occurred or exists as a result of which (i) the closing under the CCE Purchase Agreement will be delayed or (ii) any party to the CCE Purchase Agreement has, or with notice or the lapse of time or both is likely to have the right to terminate the CCE Purchase Agreement.

ARTICLE IV.

REPRESENTATIONS AND WARRANTIES OF ETE

ETE represents and warrants to ETP as follows:

Section 4.01 Existence. ETE (i) is an entity duly organized, legally existing and in good standing under the laws of its jurisdiction of organization and (ii) has all requisite power and authority, and has all governmental licenses, authorizations, consents and approvals necessary, to own, lease, use and operate its Properties and carry on its business as its business is now being conducted, except where the failure to obtain such licenses, authorizations, consents and approvals would not be reasonably likely to have a Material Adverse Effect.

Section 4.02 Authority. ETE has all necessary power and authority to execute, deliver and perform its obligations under this Agreement; and the execution, delivery and performance by ETE of this Agreement have been duly authorized by all necessary action on its part; and this Agreement constitutes a legal, valid and binding obligations of ETE, enforceable in accordance with its terms, except as such enforceability may be limited by bankruptcy, insolvency, fraudulent transfer and similar laws affecting creditors’ rights generally or by general principles of equity. No approval from the equity owners of ETE is required in connection with the transactions contemplated by this Agreement.

Section 4.03 Approvals. No authorization, consent, approval, waiver, license, qualification or written exemption from, nor any filing, declaration, qualification or registration with, any Governmental Authority or any other Person is required in connection with the execution, delivery or performance by ETE of this Agreement.

6

Section 4.04 No Breach. The execution and delivery of this Agreement by ETE, the compliance by ETE with all of the provisions of, and the performance by ETE of its obligations under this Agreement and the consummation of the transactions contemplated in this Agreement will not conflict with or result in a breach or violation of any of the terms or provisions of, or constitute a default under, (A) the constitutive documents of ETE, (B) any instrument, contract or other agreement to which ETE is a party or by which ETE is bound or to which any of its Properties or assets may be bound or subject, in each case, the breach or violation of which or default under which would be reasonably expected to have a Material Adverse Effect on the ability of ETE to comply with its obligations hereunder, or (C) any law or statute or any order, rule or regulation of any Governmental Authority and no consent, approval, authorization, order, registration, clearance or qualification or notification of, with or to any such Governmental Authority is required of ETE for the purchase of the Class G Units by ETE contemplated by this Agreement.

Section 4.05 Legal Proceedings. There are no legal or governmental proceedings pending to which ETE is a party or of which any property of ETE is the subject that, if determined adversely to ETE, would individually or in the aggregate have a Material Adverse Effect on ETE’s ability to perform its obligations under this Agreement, and, to the best of ETE’s knowledge, no such proceedings are threatened or contemplated by any such Governmental Authority or threatened by others.

Section 4.06 Nature of the Investor. ETE (a) is an “accredited investor” as defined in Rule 501(a) of Regulation D promulgated under the Act, (b) is able to bear the economic risk of losing its entire investment in the Class G Units, and (c) has knowledge and experience in financial and business matters such that it is capable of evaluating the risks and merits of this investment.

Section 4.07 Investment. ETE is acquiring the Class G Units for its own account, and not with a view to any distribution, resale, subdivision, or fractionalization thereof in violation of the Securities Act or any other applicable domestic securities law, and ETE has no present plans to enter into any contract, undertaking, agreement or arrangement for any such distribution, resale, subdivision, or fractionalization of the Class G Units. ETE acknowledges and agrees that, based in part upon its representations contained herein and in reliance upon applicable exemptions, the issuance of the Class G Units has not been registered under the Act or the securities laws of any other domestic or foreign jurisdiction and that accordingly, the Class G Units may not be offered for sale, sold, or otherwise transferred in whole or in part, except in accordance with the terms of the Partnership Agreement and in compliance with all applicable laws, including securities laws, except that the Class G Units may be pledged in a bona fide transaction.

Section 4.08 Receipt of Information. ETE has carefully reviewed the documents filed by ETP with the Commission under the Exchange Act within the 18 months prior to the date of this Agreement, including ETP’s Annual Reports on Form 10-K, Quarterly Reports on Form 10-Q, current reports on Form 8-K and other filings (the “Partnership Information”) and acknowledges that ETP has provided to ETE or its representatives all agreements, documents, records and books that ETE or its representatives have requested relating to an investment in ETP.

7

ARTICLE V.

COVENANTS

Section 5.01 Other Agreements.

(a) ETP hereby agrees to prepare and cause to be filed with the Commission a proxy statement providing for the submission for approval of ETP’s common unitholders a proposal to convert the Class G Units to Common Units on a one-for-one basis as specified in Amendment No. 10 (the “Proxy Statement”).

(b) Each party agrees that it will indemnify and hold harmless the other party from and against any and all claims, demands, or liabilities for broker’s, finder’s, placement, or other similar fees or commissions incurred by such party or alleged to have been incurred by such party in connection with the purchase of the Class G Units or the consummation of the transactions contemplated by this Agreement.

Section 5.02 Information. ETE shall supply such information with respect to itself, its directors, officers and shareholders as ETP may reasonably request for the purpose of preparation of the Proxy Statement. ETP shall supply to ETE such information with respect to itself, its directors, officers and unitholders, Transwestern and such other matters as ETE may reasonably request for the purpose of preparation of any notice, form or other documents required to be filed with any Governmental Authority in connection with the transaction contemplated by this Agreement.

Section 5.03 Further Assurances. Each party agrees to execute, acknowledge and deliver such further instruments and to do all such other acts as may be necessary or appropriate to carry out the purposes and intent of this Agreement.

ARTICLE VI.

MISCELLANEOUS

Section 6.01 Interpretation and Survival of Provisions. Article, Section and Exhibit references are to this Agreement, unless otherwise specified. All references to instruments, documents, contracts, and agreements are references to such instruments, documents, contracts, and agreements as the same may be amended, supplemented, and otherwise modified from time to time, unless otherwise specified.

Section 6.02 No Waiver; Modifications in Writing.

(a) Delay. No failure or delay on the part of any party in exercising any right, power, or remedy hereunder shall operate as a waiver thereof, nor shall any single or partial exercise of any such right, power, or remedy preclude any other or further exercise thereof or the exercise of any right, power, or remedy. The remedies provided for herein are cumulative and are not exclusive of any remedies that may be available to a party at law or in equity or otherwise.

(b) Specific Waiver. Except as otherwise provided herein, no amendment, waiver, consent, modification, or termination of any provision of this Agreement shall be effective unless signed by each of the parties hereto or thereto affected by such amendment,

8

waiver, consent, modification, or termination. Any amendment, supplement or modification of or to any provision of this Agreement, any waiver of any provision of this Agreement, and any consent to any departure by any party hereto from the terms of any provision of this Agreement shall be effective only in the specific instance and for the specific purpose for which made or given.

Section 6.03 Binding Effect; Assignment.

(a) Binding Effect. This Agreement shall be binding upon ETP, ETE, and their respective successors and permitted assigns. Except as expressly provided in this Agreement, this Agreement shall not be construed so as to confer any right or benefit upon any Person other than the parties to this Agreement, and their respective successors and permitted assigns.

(b) Assignment of Class G Units. All or any portion of ETE’s Class G Units purchased pursuant to this Agreement may be sold, assigned or pledged by ETE, subject to compliance with applicable securities laws.

Section 6.04 Assignment of Rights. All or any portion of the rights and obligations of ETE under this Agreement may not be transferred by ETE without the written consent of ETP.

Section 6.05 Costs and Expenses. Each party hereto shall be responsible for the payment of the costs and expenses incurred by it in connection with the negotiation, execution, delivery and performance of this Agreement and the transactions contemplated hereby.

Section 6.06 Notices. All notices and demands provided for hereunder shall be in writing and shall be given by registered or certified mail, return receipt requested, telecopy, air courier guaranteeing overnight delivery or personal delivery to the following addresses:

Energy Transfer Partners, L.P.

8801 South Yale Avenue, Suite 310

Tulsa, Oklahoma 74137

Facsimile: 918 ###-###-####

Attention: H. Michael Krimbill

Energy Transfer Equity, L.P.

2828 Woodside Street

Dallas, Texas 75204

Facsimile: 214 ###-###-####

Attention: John W. McReynolds

or to such other address as ETP or ETE may designate in writing. All notices and communications shall be deemed to have been duly given: at the time delivered by hand, if personally delivered; upon actual receipt if sent by certified mail, return receipt requested, or

9

regular mail, if mailed; when receipt acknowledged, if sent via facsimile; and upon actual receipt when delivered to an air courier guaranteeing overnight delivery.

Section 6.07 Governing Law. This Agreement will be construed in accordance with and governed by the laws of the State of Delaware without regard to any otherwise applicable principles of conflicts of laws.

Section 6.08 Entire Agreement. This Agreement and the other documents referred to herein are intended by the parties as a final expression of their agreement and intended to be a complete and exclusive statement of the agreement and understanding of the parties hereto in respect of the subject matter contained herein and therein. This Agreement and the other documents referred to herein supersede all prior agreements and understandings between the parties with respect to such subject matter.

Section 6.09 Counterparts. This Agreement may be executed in any number of counterparts and by different parties hereto in separate counterparts, each of which counterparts, when so executed and delivered, shall be deemed to be an original and all of which counterparts, taken together, shall constitute but one and the same Agreement.

Section 6.10 Equitable Relief. Each party hereto agrees that money damages would not be a sufficient remedy for any breach of this Agreement by either party hereto or their respective Representatives and that the non-breaching party shall be entitled to equitable relief, including injunction and specific performance, in the event of any such breach, in addition to all other remedies available to the non-breaching party at law or in equity. Each party further agrees to waive any requirement for the securing or posting of any bond in connection with such remedy.

[Signature page follows]

10

IN WITNESS WHEREOF, the parties hereto have caused this Agreement to be duly executed, as of the date and year first above written.

SIGNATURE PAGE TO

CONTRIBUTION AND CONVEYANCE AGREEMENT

EXHIBIT A

AMENDMENT NO. 10 TO PARTNERSHIP AGREEMENT

EXHIBIT A

EXHIBIT B

CERTIFICATE LEGEND

THIS SECURITY HAS NOT BEEN REGISTERED UNDER THE SECURITIES ACT OF 1933, AS AMENDED. IT MAY NOT BE SOLD, OFFERED FOR SALE, PLEDGED OR HYPOTHECATED IN THE ABSENCE OF A REGISTRATION STATEMENT IN EFFECT WITH RESPECT TO THE SECURITIES UNDER SUCH ACT OR AN OPINION OF COUNSEL SATISFACTORY TO THE PARTNERSHIP THAT SUCH REGISTRATION IS NOT REQUIRED.

EXHIBIT B

EXHIBIT C

REGISTRATION RIGHTS AGREEMENT

EXHIBIT C