Well, my ex-boyfriend and I have been in and out of court for 5 1/2 years and it is a total nightmare. If you choose not to put the father on the birth certificate, he still has rights to the child as soon as paternity is filed. If he is not interested in having the baby - hooray for you - immediately have documents drawn up to sign all his parental rights away. I did not do this - I forced him to be a father by going to court to make him have visitation. Well, then he got married and his wife got in the business and we have been in and out of court ever since because he wants more visitation and pay less child support. His motives for visitation are all wrong. I am now happily married and have a 10 month old son. My daughter (7 years old) is drug through the middle of her father and I. If I had known then that he could sign his rights away, I would have done it in a minute. It makes more options later on in life for stability and adoption.
I feel that divorced couple go to court once for visitation - when the divorce is taking place. For me not to be married, he can take me back as many times as he chooses. California needs to have better laws with major restrictions.
Good Luck and remember the choice you make now might hurt for a little bit, but it will make the future easier. I learned that the hard way.