A Voluntary Acknowledgement of Parentage (VAP) is a legally-binding document that establishes one's legal parentage for a child.
If you are present with the biological mother at the hospital when a child is born, and the two of you are not married, you will likely be given the choice of signing a VAP. You may also request to sign a VAP for a child contacting the Department of Family Services (HFS), but only if the child does not already have two legal parents.
If a signed VAP is approved, the name of the signee will be placed on the child's birth certificate.