First off, I am single.second,I am the father of a beautiful baby girl. Back when she was born I didn't have my name put on the birth certificate because if she wasn't mine I didn't want to be legally responsible for her. Well, a paternity test proves she's my daughter and I've been trying to get my name on the certificate since.I'm paying child support and establishing a wonderful relationship with her but The offices where I got the papers are zero help as far as getting my name on the birth certificate and I'm wondering if it's all that important to do this... As long as I have the paternity test papers, don't I have all the same rights as the mother?

No you don't have ALL the same rights. You have sperm donor rights. If you want full rights you have to go through the courts and have them order your name to be put on the birth certificate. Right now if you were to travel what you have isn't enough for anything. Sorry but you need to finish what you have started. Good Luck.