You need to talk with a lawyer, because some of the advice that is being given here is highly inaccurate. For example, birth certificates do not necessarily guarantee that dad has any powers. In my state (and I am a licensed attorney here) a man's name on a birth certificate doesn't mean anything legally at all because a mom can just add whoever they want to the birth certificate. In order for a father, who was and is not married to the mom at the time of conception and birth, to obtain any legal rights to the child he has to go to court and file a petition for adjudication of paternity OR him and mom have to agree to file an "Acknowledgment of Paternity" with the State's vital statistics unit.

A quick consult ($150-$200 usually, but sometimes you can get one for free) with a family attorney in your area will give you the answers relevant to your State of residence. Do this ASAP as it can take a while to get into an attorney's schedule. (EDIT: family attorneys deal with this issue often enough that they should be able to ask you all of the relevant questions and get enough information from you to let you know right then and there if you need to do anything special; their intake process should ask you to gather what documentation they need to give you an answer).