My son and girlfriend have lived together 5 years not married ,they have two small boys now they are splitting up and she wants to move the boys out of state .How can he stop this . He is on the birth certificate and has been they total support

He has to file for joint (or full) custody with visitation rights. He has to get the court to order visitation rights on a regular basis. This will prevent the mother from moving if it will interfere with visitation.