N.M. Stat. § 19-3-14
Whenever any person, company or corporation turns loose on any range in this state, already occupied or in the possession of another or others by virtue of their having complied with the provisions of the preceding section [19-3-13 NMSA 1978], he or they must be the owner or owners of, or must be lawfully entitled to the possession of some other living, permanent water upon such range, sufficient for the proper maintenance of all such additional cattle so turned loose, other than that owned by or lawfully possessed, or lawfully in the possession of any other person, company or corporation that may have previously appropriated, stocked or taken possession of such range in accordance with the provisions of this and the preceding section; and such person, company or corporation so turning loose cattle upon such range must at all times, furnish, supply and maintain upon such range such other permanent living water free and unfenced and upon the surface of the ground.
NMS § 19-3-14