N.M. Stat. § 19-4-8
Such corporate authorities or probate judge, holding the title of such lands in trust, as declared in the said act of congress, his or their successors shall, by a good and sufficient deed of conveyance, grant and convey the title to each and every block, lot, share or parcel of the same to the person or persons who shall have possession, or be entitled to the possession or occupancy thereof, according to his, her or their several and respective rights or interest in the same, as they existed in law or equity at the time of the entry of such lands, or to his, her or their heirs and assigns. Every such deed to be made by such corporate authorities, or by such probate judge, shall be so executed and acknowledged as to admit the same to be recorded.
NMS § 19-4-8