<PAGE>

                                                                   EXHIBIT 10.34

                     ASSIGNMENT OF NEO DEBT AND COLLATERAL

     This Assignment of Neo Debt and Collateral (this "Assignment") is made as
of the 21/st/ day of December, 2000 by and between Crosby Capital LLC, a Texas
limited liability company ("Assignor"), and Aviva Operating Company, a Delaware
corporation ("Assignee").

                                    RECITALS
                                    --------

     WHEREAS, Assignor, Aviva Petroleum Inc. ("Parent"), Assignee and certain
other parties entered into a Loan, Settlement and Acquisition Agreement dated as
of the 31/st/ day of May, 2000 (the "LSAA");

     WHEREAS, terms not otherwise defined herein shall have the meanings
assigned to those terms in the LSAA;

     WHEREAS, under the provisions of Section 3.01(b) of the LSAA, Assignor
granted to Parent the option to acquire all of Assignor's right, title and
interest in and to the Neo Debt and Collateral (the "Option") in consideration
for the assignment to Assignor of the NPI pursuant to the form of Net Profits
Agreement attached as Exhibit B to the LSAA with Aviva America's obligations
under the Net Profits Agreement being secured by the form of Mortgage attached
as Exhibit C to the LSAA;

     WHEREAS, Parent exercised the Option on November 17, 2000 and provided
notice to Assignor that the assignment of the Neo Debt and Collateral pursuant
to the provisions of Section 3.01(b)(iv) was to be made to Assignee, as Parent's
designee;

     WHEREAS, Assignor is executing this Assignment to convey to Assignee all
Assignor's right, title and interest in and to the Neo Debt and Collateral under
the Loan Documents subject to the provisions of Section 3.01(b)(iv) of the LSAA.

     NOW, THEREFORE, in consideration of the promises contained herein and other
good and valuable consideration, the receipt and sufficiency of which are hereby
acknowledged, and intending to be legally bound hereby, the parties agree as
follows:

     1.   Assignment of Neo Debt and Collateral.  Assignor hereby conveys,
          -------------------------------------
transfers, assigns, grants, sells and delivers, to Assignee, and Assignee
acquires, accepts and purchases, all of Assignor's right, title and interest in
and to the Neo Debt and the Collateral under the Loan Documents; provided that
immediately prior to the transfer of the Neo Debt and Collateral under the Loan
Documents hereunder to Assignee, Assignor has released all security interests
and Liens under the Loan Documents in (a) the Partnership Interest and assets of
Argosy International and (b) the NPI being assigned contemporaneously herewith
to Assignor.

     2.   Delivery of ING Note and Collateral.  Contemporaneously herewith,
          -----------------------------------
Assignor is delivering to Assignee (a) an Affidavit of Lost Amended and Restated
Promissory Note and (b) the original stock certificates in Assignor's possession
evidencing the ownership of the following entities, together with irrevocable
stock powers endorsed to Assignee: Aviva America, Inc.; Aviva Delaware, Inc.;
Aviva Operating Company; Aviva Merger, Inc.; Aviva Energy Inc.; London &
Aberdeen, Inc.; Neo Energy, Inc.;
<PAGE>

Southwest Texas Salt Water Disposal Company; Garnet Pakistan Corporation; Garnet
P&G Corporation; Garnet Spain Corporation; Garnet Resources Corporation; Garnet
Resources Canada Ltd.; Garnet Turkey Corporation; and Garnet Sulfur Company.

     3.   Representations of Assignor.  Assignor represents and warrants that it
          ---------------------------
is the legal and beneficial owner of, and has good right, title and interest in
and to the Amended and Restated Neo Note being assigned, sold and transferred by
it to Assignee hereunder and that such right, title and interest is free and
clear of any lien, security interest, pledge, claim, charge, encumbrance or
adverse claim, other than as provided by the Loan Documents.  Assignor
represents that it is the legal and beneficial owner of, and has the right,
title and interest in and to the Loan Documents, as transferred to it by ING
(U.S.) Capital LLC, a Delaware limited liability company ("ING"), and the
Overseas Private Investment Corporation, an agency of the United States of
America ("OPIC"), pursuant to the Loan and Equity Sale Agreement, dated as of
April 13, 2000 (the "Loan Sale Agreement"), by and among Assignor, ING and OPIC.
The Loan Documents are free and clear of any lien, security interest, pledge,
claim, charge, encumbrance or adverse claim, other than as provided therein or
in the Loan Sale Agreement.  Such assignment and transfer of the Neo Debt and
Collateral shall be made without representation or warranty other than in this
Section 3.  Without limitation of the foregoing disclaimer, except as set forth
in this Section 3, Assignor makes no representation or warranty and assumes no
responsibility with respect to any statements, warranties or representations
made by any person in connection with the Amended and Restated Neo Note and the
Loan Documents or the execution, legality, validity, enforceability,
genuineness, sufficiency or value of the Amended and Restated Neo Note and the
Loan Documents; and Assignor makes no representation or warranty and assumes no
responsibility with respect to the financial condition of any Related Person (as
defined in the Loan Documents) or the performance or observance by any Related
Person of any of its Obligations (as defined in the Loan Documents).

     4.   Assumption.  Assignee hereby assumes the liabilities and obligations
          ----------
of Assignor under the Loan Documents.

     5.   Further Assurances.  Assignor shall execute and deliver to Assignee
          ------------------
such further documents and instruments, and take such other action, that may be
reasonably requested by Assignee to evidence this Assignment of Neo Debt and
Collateral hereunder including, without limitation, the execution of any and all
UCC-3 financing statement assignments and any other documents or instruments
that may be necessary, desirable or appropriate to evidence the consummation of
the transactions contemplated hereby.  Assignor agrees to execute any such
additional documents or instruments within five (5) business days after receipt
of any request to do so from Assignee.  In addition, Assignor agrees to
cooperate with Assignee in attempting to provide any information in Assignor's
possession regarding the Loan Documents not previously provided to Assignee upon
Assignee's reasonable request therefore.

     6.   Inurement.  This Assignment shall be effective as of the date hereof
          ---------
and shall inure to the benefit of and be binding upon the parties hereto and
their successors and assigns.  However nothing in this Assignment, express or
implied, shall give any other person any benefit or any other legal or equitable
right or remedy with respect to hereto.
<PAGE>

     7.   Counterparts.  This Assignment may be executed in counterparts, each
          ------------
of which when so executed shall be deemed to constitute one in the same
Assignment.  Such execution and delivery may be accomplished by facsimile
transmission.

     IN WITNESS WHEREOF, each of the undersigned has caused this Assignment to
be executed as of the day and year first written above.


Witnesses:                              Crosby Capital, LLC


/s/ Stanton Eigenbrodt                  By: /s/ Jay A. Chaffee,
--------------------------------           -------------------------------
                                            Jay A. Chaffee,
                                            President
/s/ Sam A. Mills
--------------------------------


Witnesses:                              Aviva Operating Company


/s/ Barry Cannaday                         By: /s/ R. Suttill
--------------------------------           -------------------------------
                                            Ronald Suttill,
/s/ F. Broyles                              President
--------------------------------

<PAGE>

STATE OF TEXAS      (S)
                    (S)
COUNTY OF DALLAS    (S)

     On this 21st day of December, 2000, before me appeared Jay A. Chaffee, to
me personally known, who being by me duly sworn did say that he is President of
Crosby Capital, LLC, and that the instrument was signed on behalf of the same,
by authority of its Board of Directors or other governing body and that he
acknowledged the instrument to be the free act and deed of said limited
liability company.

     This instrument was acknowledged before me on the 21st day of December,
2000, by Jay A. Chaffee, the President of Crosby Capital, LLC.


                                  /s/ Gwendalyn Anne Davis
                                  -------------------------------------------
                                  Notary Public in and for the State of Texas

[STAMP OF GWENDALYN ANNE DAVIS]

My commission expires:

     8-28-01
----------------------


STATE OF TEXAS      (S)
                    (S)
COUNTY OF DALLAS    (S)

     On this 21st day of December, 2000, before me appeared Ronald Suttill, to
me personally known, who being by me duly sworn did say that he is President of
Aviva Operating Company, and that the instrument was signed on behalf of the
same, by authority of its Board of Directors and that he acknowledged the
instrument to be the free act and deed of said corporation.

     This instrument was acknowledged before me on the 21st day of December,
2000, by Ronald Suttill, the President of Aviva America Inc.



                                    /s/ Gwendalyn Anne Davis
                                    -------------------------------------------
                                    Notary Public in and for the State of Texas

[STAMP OF GWENDALYN ANNE DAVIS]

My commission expires:

     08-28-01
----------------------