A man who is not married to a child's mother does not have any parental rights until his paternity has been established. Paternity may be established by the father's acknowledgment or by a paternity test. The father may acknowledge his paternity simply by signing his name on the birth certificate or by consenting to the placement of his name on the birth certificate. In some states the father may have to submit a formal affidavit attesting to his paternity.
The information on this page is meant to provide a general overview of the law. The laws in your state and/or city may deviate significantly from those described here. If you have specific questions related to your situation you should speak with a local attorney.