Parental Rights

Hi, I am from New York State. I would like to know the difference between parental rights and visitation rights? Also, when does a father have the right to stop paying child support?

Each one of these questions should be specifically addressed in your divorce decree. Take time to read it and/or if there are things you don't understand contact your attorney and he/she will explain them to you.
Custody laws are pretty much straight forward although they will vary from state to state depending on the law.
Basically, child support can only be stopped by court order, death of the child or when the child reaches maturity, usually 18-21 years of age. This varies from state to state also. Some courts put in a provision protecting the child if they go to college but is capped at 22 years of age. But again this varies from state to state and court to court.

Best advice I have is to talk with your attorney.

Good luck