N.M. Stat. § 72-1-2

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.