What is the legal process to be my girlfriends unborn child's father?

I willing started a relationship with a girl I had gone to school with. I knew she was pregnant from someone else, she did not want to, but the guy is a jerk and did it anyway. She doesn't want him near her or the baby. He is a high-school dropout, and never had a job. She is due around May. I have been out of school for a couple of years, and have had a full time job since. I am wanting to care for her and the baby. I would like to become the father. I was told something about just signing the birth certificate when the child is born, but I want to be able to make sure I know the whole process, and how the sperm donor can not have any rights to be around the baby.