Dead Beat/Absent Parents

I would like to start a petition for parents who are primary care givers to minor children. I feel that if the absent parent never pays child support, or is not in any contact with the minor child that the primary care giver should be given full custody over the child. In my situation my daughters father walked out when she was 2 years old, she is now almost 11, he walked out, never pays child support, has had a warrant for non-payment for 3 years now,.he also has not tried to contact either of us to even check on her. I wanted to change her last name to mine and the courts told me that I needed the father's permission. I was shocked. How can a person who has absolutely No hand in raising or taking care of the child be the person I need permission from? I was also told by that court that because the fathers name was on the birth certificate that he could come and pick her up right out of my front yard without my permission and that if I called the police there would be nothing they could do because he is her father. That is a scary thing for any parent to think about. The law needs to be changed, if you are a dead beat/absent parent then you should not have any so say regarding the child.