Blower fan runs on high

My blower fan runs on high despite me switching to low or automatic (it is a automatic climate control). I turned the car off, and the fan kept blowing on high. I finally pulled the wire on the blower fan to keep from draining the battery.

I never heard of a fan run by itself before so I'm thinking it's the relay (contacts stuck in on position). I would be very happy to have a second or third opinion.

I haven't checked the fuses for the obvious reason the fan is working and not stopping.