N.M. Stat. § 73-1-15

Upon the filing of a petition as provided for in Section 1 hereof, the district court having jurisdiction shall, by order, require notice to be published by the clerk of the court, at such time and places as the court may designate, giving notice to all landowners affected by the proposed change that a hearing will be had at a time and place designated in such notice, for the purpose of determining whether or not all of the lands described in the certificate of the state engineer filed with the said petition should be included in the artesian conservancy district, and the decree establishing the district amended accordingly. It shall not be necessary for the clerk to name the parties interested, nor to describe the separate lots, tracts or parcels of land affected in giving such notice, but it shall be sufficient to give such description of the lands proposed to be included as will enable the owner to determine whether or not his land is covered by such description.

The notice shall state that any person affected by the proposed inclusion of such lands shall have the right to file objections thereto, on or before the date set for hearing. If, after hearing such objections, if any, and considering any evidence introduced in support thereof, the court finds that the said lands described in the petition should be included within the said artesian conservancy district, the court shall enter an order amending said decree, as prayed for in said petition, and thereupon said lands shall be included within the said conservancy district and shall be subject to the same rights, powers and authority as given by law to such artesian conservancy district over lands located within said district.