“Do you breathe on your own with general anesthesia?”

It depends on what kind of surgery you are having.Most surgeries your breathing is taken over by ventilator and you resume breathing at end of surgery.

Depending on the type of surgery you are having, your surgeon may require that you are perfectly immobile during surgery, and in that case you will be paralyzed and your anesthesiologist will control you breathing. In other kinds of surgery where your surgeon does not require paralysis, your anesthesiologist may keep you asleep while you breathe anesthetic gases spontaneously on your own.

Usually during general anesthesia, you are paralyzed and do not breathe by yourself. But in some short procedures, you could breathe assisted by an anesthesiologist.