N.M. Stat. § 19-10-13
All leases issued under the provisions of this act [19-10-1, 19-10-12 to 19-10-25 NMSA 1978] shall be assignable in whole or in part; provided, however, that no assignment of an undivided interest in the lease or any part thereof, or any assignment of less than a legal subdivision shall be recognized or approved by the commissioner.
The term "legal subdivision" as used in this act shall be construed in its ordinary sense as used and recognized in the general land office of the United States and in the state land office of New Mexico. The assignments provided for herein shall be executed and acknowledged in the manner prescribed for conveyance of real estate in this state and shall be filed in triplicate in the office of the commissioner who shall retain two copies of the said assignment in his office as a public record and shall record one of same in permanent form in his office as a public record and shall return one of the duplicate copies to the person entitled thereto. The approval of the commissioner shall be noted upon all copies of the said assignment. The commissioner shall prescribe the form to be used for such assignments and shall fix a reasonable fee for the filing, recording and approval of same. The commissioner shall have the right to refuse approval of any assignment not executed in proper form or by the proper person or persons, or when the lease is not in good standing as to the assigned tracts, or when litigation is pending affecting the lease or the interest of any person therein. Upon approval by the commissioner of an assignment the assignor shall stand relieved from all obligations to the state with respect to the lands embraced in the assignment and the state shall likewise be relieved from all obligations to the assignor as to such tract or tracts, and thereupon the assignee shall succeed to all of the rights and privileges of the assignor with respect to such tracts and shall be held to have assumed all of the duties and obligations of the assignor to the state as to such tracts. Provided, however, the record owner of any oil and gas lease may enter into any contract for the development of the leasehold premises or any portion thereof, or may create overriding royalties or obligations payable out of production, or enter into any other agreements with respect to the development of the leasehold premises or disposition of the production therefrom, and it shall not be necessary for any such contracts, agreements or other instruments to be approved by the commissioner of public lands; but nothing herein contained shall relieve the record title owner of such lease from complying with any of the terms or provisions thereof, and the commissioner shall look solely and only to such record owner for compliance therewith, and in any controversy respecting any such contracts, agreements or other instruments entered into by such lessee with other persons the state of New Mexico or the commissioner of public lands shall not be a necessary party. All such contracts and other instruments may be filed either in the office of the commissioner of public lands or recorded in the office of the county clerk of the county where the lands are situated, and the filing or recording thereof shall constitute notice to all the world of the existence and contents of the instruments so filed or recorded. The commissioner may prescribe a reasonable fee for the filing of such instruments in the office of the commissioner of public lands.
The discovery of oil or gas upon lands embraced in any state lease shall continue such lease as to all of the lands embraced therein for as long thereafter as oil and gas in paying quantities or either of them is being produced in accordance with the provisions thereof regardless of any assignment of all or any portion of the lease which may have been made prior or subsequent to the discovery of such production.
NMS § 19-10-13