I have had my 2003 Z71 silverado for about a year and I am about to put some new tires on. Does anyone know what the tallest and widest size tire that can fit wit the torsion bars all the way up? Thanks in advance.

285s.

285/75R16 gives you tall with a stock look in width.
305/70R16 gives you tall with a wider look in width.
Both tires are 33 inches tall.
I like the 305's for flotation purposes in sand and other off-road applications.

Do the 305/70R16 rub at all when turning?

Yeap, 305s will be too big. 285s will almost rub. but you will still be able to use them.

If you want to go with 305s you'll probably have to do some cutting on your front valance.

The only time 305's rub and the only place is inside the fender where the fender trim is. With a few good rubs, it won't rub any more. Or you could alway bend the fender lip a little, it's on the inside, no one can see. I've used 305's for about 5 years now.