What papers do I fill out to get physical custody of my child?

The answer to your question really depends on the County of the Child's residence and your "parental" status.  If you have not legitimated the child, then you will need to do that first, to get parental rights to even request custody.  You will have to petition the court for legal rights (either through legitimation or if this is a divorce, then either as a divorce proceeding or a modification if necessary).  Whichever way, most clerk's offices have packets of forms.  You will need a petition, child support worksheets, financial affidavit and a parenting plan.  If you are legitimating, then most counties require DNA test results.  If the custody becomes contested, you might have to hire a Guardian or Custody Evaluator.  You should strongly consider hiring an attorney to assist you, or at the very least a mediator to assist in resolving the case before too much time passes and the case gets expensive.