N.M. Stat. § 72-1-2
[Water rights; appurtenant to land; priorities.]
Beneficial use shall be the basis, the measure and the limit of the right to the use of
water, and all waters appropriated for irrigation purposes, except as otherwise provided
by written contract between the owner of the land and the owner of any ditch, reservoir
or other works for the storage or conveyance of water, shall be appurtenant to specified
lands owned by the person, firm or corporation having the right to use the water, so long
as the water can be beneficially used thereon, or until the severance of such right from
the land in the manner hereinafter provided in this article. Priority in time shall give the
better right. In all cases of claims to the use of water initiated prior to March 19, 1907,
the right shall relate back to the initiation of the claim, upon the diligent prosecution to
completion of the necessary surveys and construction for the application of the water to
a beneficial use. All claims to the use of water initiated thereafter shall relate back to the
date of the receipt of an application therefor in the office of the territorial or state
engineer, subject to compliance with the provisions of this article, and the rules and
regulations established thereunder.