N.M. Stat. § 19-4-33
Whenever the title to any such lands shall be vested in any probate judge, he shall convey to the proper or legal authorities so much of the land as is or shall be laid out by the town authorities into streets, lanes, avenues, parks, public grounds and commons, within the time prescribed in this chapter for making conveyance to individuals. But when the title to such lands shall be held by the corporate authorities of any town, all land used, laid out or designated for public use by such corporate authorities, as streets, lanes, avenues, alleys, parks, commons and public grounds, shall vest in and be held by the corporation absolutely, and shall not be claimed adversely by any person or persons whosoever [whomsoever], and it shall not be necessary to execute any conveyance for the same to the corporation or people of such town.
NMS § 19-4-33