The court may terminate a parent's rights to a child who is the subject of an adoption proceeding based upon:
(1) the voluntary acts of the parent in:
(a) executing a voluntary relinquishment and consent to adopt;
(b) submitting a notarized denial of paternity executed pursuant to 42-2-421; or
(c) submitting a notarized acknowledgment of paternity and denial of interest in custody of the child executed pursuant to 42-2-422;
(2) a determination under 42-2-608 that the parent is unfit;
(3) a determination under 42-2-609 that the relationship of parent and child does not exist;
(4) a determination under 42-2-610 that a putative father has failed to establish and maintain a substantial relationship with the child; or
(5) a determination that the parent has irrevocably waived parental rights by failing to timely act to protect the rights.