N.M. Stat. § 45-2-114
Parent barred from inheriting in certain circumstances.
A. A parent is barred from inheriting from or through a child of the parent if:
(1)
the parent's parental rights were terminated and the parent-child
relationship was not judicially reestablished; or
(2)
the child died before reaching eighteen years of age and there is clear and
convincing evidence that immediately before the child's death the parental rights of the
parent could have been terminated under law of New Mexico other than the Uniform
Probate Code on the basis of nonsupport, abandonment, abuse, neglect or other
actions or inactions of the parent toward the child.
B. For the purpose of intestate succession from or through the deceased child, a
parent who is barred from inheriting under this section is treated as if the parent
predeceased the child.