At any hearing to determine the parental rights of an adjudicated biological father or putative biological father of a minor child born out of wedlock and whether such father's consent is required for the adoption of such child, the court shall receive evidence with regard to the actual paternity of the child and whether such father is a fit, proper, and suitable custodial parent for the child. The court shall determine that such father's consent is not required for a valid adoption of the child upon a finding of one or more of the following:
(1) The father abandoned or neglected the child after having knowledge of the child's birth;
(2) The father is not a fit, proper, and suitable custodial parent for the child;
(3) The father had knowledge of the child's birth and failed to provide reasonable financial support for the mother or child;
(4) The father abandoned the mother without reasonable cause and with knowledge of the pregnancy;
(5) The father had knowledge of the pregnancy and failed to provide reasonable support for the mother during the pregnancy;
(6) The child was conceived as a result of a nonconsensual sex act or an incestual act;
(7) Notice was provided pursuant to sections 43-104.12 to 43-104.14 and the putative father failed to timely file a Notice of Objection to Adoption and Intent to Obtain Custody pursuant to section 43-104.02;
(8) The putative father failed to timely file a petition to adjudicate a Notice of Objection to Adoption and Intent to Obtain Custody pursuant to section 43-104.05;
(9) Notice was provided to an adjudicated biological father through service of process under applicable state law and he failed to object to the adoption or failed to appear at the hearing conducted under section 43-104.25;
(10) The father executed a valid relinquishment or consent to adoption; or
(11) The man is not, in fact, the biological father of the child.
The court shall determine the custody of the child according to the best interest of the child, weighing the superior rights of a biological parent who has been found to be a fit, proper, and suitable parent against any detriment the child would suffer if removed from the custody of persons with whom the child has developed a substantial relationship.