Can I get custody of my nephew if the mother asked me to get him and I said I wasn't going to keep him if I do and she said OK I don't care long as I can get visits?

Not unless you go to court and have them award it to you...

Hire a lawyer and give it a try.

The mother can legally give you guardianship if that is what she wants. But either way, like smoothy said, you have to go through the court system.