Does being granted sole custody terminate court ordered child support in California?

I was never married to my childs father and have a court order for child support. He does not pay his child support and is in arrears. I can not rely on him to cooperate in making decisions for our child and he has very limited contact with her neither through visitation nor phone calls. I am not trying to prevent him from seeing her but need to establish my legal right to make decisions without his imput when necessary.