A common size on a medium-duty-truck lug-nut "star wrench" is 1-1/16". It's what I used today to remove my 1999 water heater's anode rod. Since the anode was at "zero material", I suspect it had never-before been serviced. The tank had lots of chunks of white crud, which mostly washed out with a wand made for that purpose.
I got out a 3/4" pipe tap, and with the aid of a 13/16" twelve-point socket, extension, and drive was able to "chase" the threads in the tank. Didn't really cut the threads any deeper, but got rid of most of the rust in them.
A few layers of thin teflon tape on the new anode rod's threads and it went back into the tank with ease. It didn't require a lot of torque to effectively seal against the pressure.
If you're having problems removing an old rod, I highly recommend finding a cross-star lug wrench that has a 1-1/16" size. You WILL get it out.