N.M. Stat. § 19-4-31
At any time after the expiration of ninety days from the time of first publication of the notice mentioned in Section 19-4-9 NMSA 1978, the corporate authorities or probate judge shall, upon demand or request and payment as required by Section 19-4-26 NMSA 1978, execute and deliver to each and every claimant, or association, or company of claimants to such lands or any parcel thereof, a deed of conveyance therefor, according to the statement made and deposited by him or them, pursuant to Section 19-4-10 NMSA 1978: provided, however, that no such deed of conveyance shall be executed or delivered for any part, portion or share of such lands, to which there shall be adverse contesting claimants, until the controversy thereon has been settled and determined in the manner described in this chapter.
NMS § 19-4-31