If my name is on the title to a car, am I responsible for n over 18 child if they gets in an accident?

Yes, if your name is on the title of the car, you can be help responsible for any damages that may arise as a result of the vehicle being in an accident.  If you have insurance, your insurance should cover damages for you, however, in general, you can be liable for damages if you vehicle is involved in an accident, whether you were driving or not.