Heater fan runs constantly on high,with ignition switch on or off,and fan switch in any position.

check for bad relay had a similar problem

I'm willing to bet $100 it's the fan switch itself. That is the switch on the dash that you use to adjust the fan speed. Very common. Don't let the dealership sell you the control assembly. They can sell you just the swith. Should cost $15 to $20 (plus the $100 when you see I was correct)