what would cause an alternator to output 21vdc?

**replace the alt***...you can run/have a 16 volt system but not in your car unless changed...we run 16 volts now in our hot rods. when they go /low/dead we still have 12 volts...but dont spread that around....but,,,More or less, a car charges from 13.8 to 14.4 volts... A true deep cycle battery can take charging in the 14.8 volt to 15.5+ volt range (fast charging), and 15-16+ volts for equalization. you could take the alt to a alt/starter/generator shop and change the reg.also..

I concur you should change the alternator if I am correct it means their is some sort of short in th alternator. I had a similar issue i rebuilt the alternator and I was all set.