Legal Question in Family Law in New Mexico

If you intend to keep the house your ex will have to buy him/herself out. Starting with an appraisal to determine the current value of the house. The order of names on the mortgage doesn't mean anything, unless there is some qualification associated with each name. Are you listed as joint tenants or tenants in common? Did you split the payments equally or did one contribute more than the other? Was there an agreement that one would make payments in exchange for some other service by the other? All those things would come into consideration in a courtroom to determine the ownership. There's no equivalent to the community property laws that govern property splits in divorces, in New Mexico, for domestic partners that I know of, so absent an agreement between you concerning the house, you'll have to determine what's fair by some means you both agree on, or by going to court and letting a judge decide (bad and expensive idea, if you can avoid it).