If general anethesia is given to a patient through an iv, do they still breathe on their own?

It depends what you: Mean. If enough IV drugs are used, patient will stop breathing, so they need assisted ventilation, usually with a mask and for few minutes only. But these patients usually don't have a breathing (endotracheal) tube, which is used when breathing is completely stopped for longer periods. When IV drugs are stopped or reversed, the patient usually starts breathing spontaneously after a few minutes.

Under general: Anesthesia, sometimes patients breathe spontaneously, sometimes their ventilation is assisted or controlled.

General anesthesia: He could if surgery does not require complete relaxation of the muscles and if the amount of opioid is not too much. There are methods of general anesthesia during which the patient is breathing by himself, but only the anesthesiologist can decide if it is safe for the patient or not to do that.

Sometimes: Most of the time the patient is started on anesthesia with an iv. Once that has taken effect the anesthesiologist will take over for you and put you on a breathing machine. This is for your safety, as it is very easy to stop breathing under anesthesia. Rarely will a patient be asleep under general anesthesia while breathing on their own. Talk to your anesthesiologist for more information.

If I want them to: Sometimes they do and sometimes they don't. If it is "sedation" idea is you breathe. For general anesthesia u can be breathing with or without support. Think of a boxer knocked out in the ring breathing but people slapping his face and he doesn't wake up.