Legal question: child custody with a few twists

I come before you once again with a fictional scenario for which I'd like some factual information. We're in the legal realm this time. I know only a little law (for instance, I'm pretty sure it's illegal to run someone over with your car without giving them your insurance information beforehand), so feel free to use small words in your answer.

Scenario: a woman is pregnant and does not want to keep the child herself. She has agreed to let the father, her ex-boyfriend, take the baby. For what ...