[MamaS]

I don't know about other states, but I do know about Georgia. When my first grandchild was born, his mother was unmarried, under 21, and under my insurance. Before we were allowed to leave the hospital, I had to sign a statement that I would be responsible for all of the BABY'S expenses, in the event they were not covered by the insurance company. That included circumcision, time under a sunlamp for jaundice, etc.
My second daughter was covered by Medicaid when her baby was born, but again, before they left the hospital she had to sign a statement that she would accept responsibility and personally pay all charges for the baby that were not paid by Medicaid.
Neither of these babies were adopted out, but it seems reasonable that the hospital, if it were aware of PAPs, would ask them to sign before the baby leaves. Then, if doesn't matter to the hospital whether the mother chooses to parent or not -- they have a signed agreement from someone to pay the balance, period!