What is the age the child can leave the home in new york and not be considered a runaway?

It's considered running away if your parents are not aware of your wherabouts. I think if you just wander out the door after about your sixteenth birthday they'll assume you can take care of yourself.

I don't think you are actually legally allowed to move out until you are legally an adult though: eighteen.

I'm not sure if you are talking about moving out or just wandering off . . . please clarify.