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31x10.5x15 gets awfully close with a load of fire wood, but it just squeaks by the fender in the back. That's with a 8 inch aftermarket rim. If you run a stock rim, that size tire will rub the radius arm up front in the parking light.
11 inches with the 7.5 inch rim. I know; I used to run 27x11's. Seems like 11.5's are possible, but I don't know for sure. I do know 11 inches will work.
It really depends on how you use the truck. With an actual load on a stock rim a 10.5 is about as big as you can get as franklin said.
No load, just as a play toy 12.5's look real good on a stock rim, stick out just a little.
Now if you start offsetting the wheel in towards the frame, you can pick up a bunch more.
I've run a 12.5 on a stock rim and it stuck out past the fender about 1" at the top. Keeping the lip in mind, you'd be at a 10.5 to actually get the tire in the wheel well with NO rubbing.