I'm not going to put him on the birth certificate. I'm willing to take a paternity test, and if he is the father, I'm totally willing to let him see her. I just want to know, does he have the right to demand a paternity test whenever he wants? Or can I wait for a couple weeks after I have my baby? How soon can he take me to court? Thanks for answering, and please let me know any extra details!

He cannot take you to court until after the baby is born. At that point he can take you to court any time he wants.