N.M. Admin. Code § 18.11.2.11
Whenever the owner or lessee of a registered aircraft transfers title or interest therein, the registration certificate and number issued for such registration shall remain with the aircraft. Upon transfer or assignment of title or interest, the owner or lessee shall endorse such assignment on the reverse side of the certificate of registration, which statement shall be verified under oath by such owner or lessee. The owner or lessee shall deliver the certificate of registration and the registration number to the purchases or transferee at the time of delivery of the aircraft. The purchaser or transferee shall, within ten (10) days from the date of transfer, submit the endorsed certificate to the Division. The Division will issue a new certificate at a charge of $5.00. If an aircraft is not registered at the time of purchase or lease, even though the aircraft my have been purchased within the State, new or used, the purchaser shall register it as provided herein together with all penalties due.
N.M. Admin. Code § 18.11.2.11