Your question is a bit fuzzy. Our custody laws are gender neutral -- there is no custodial preference for mothers or fathers based solely on that status.
Each parent has an independent obligation of support, which (if I understand your question) persists until the child is adopted, if ever. Whether a bio father has any custodial rights depends on whether he is a legal father -- by signing an affidavit of paternity at the birth of the child, or being adjudicated the father in a paternity action. If this is not clear, consider the resources posted at:
http://willicklawgroup.com/child-custody-and-visitation/
http://willicklawgroup.com/child-support/
http://willicklawgroup.com/paternity/
Answered on Aug 01st, 2014 at 2:15 PM