(a) A surviving parent is not entitled under § 3-104 of this subtitle to a distribution of the net estate of a minor child of the parent if the parent:

(1) Abandoned the child; or

(2) Willfully failed to contribute to the support of the child for at least 3 consecutive years immediately preceding the death of the child or for the life of the child, whichever is less.

(b) A parent shall be deemed to have abandoned a minor child under subsection (a)(1) of this section if the conduct of the parent demonstrates a settled purpose willfully and intentionally to relinquish all parental rights and duties with respect to the child and to renounce and forsake the child entirely.