Rear tire width requirements in relation to HP?

Physics wise the friction doesn't change a bit because of the size of the contact patch. Real world, the wider and especially taller tire will help as it deals with imperfections in the road and heat better then the skinny tire. Most likely it's the compound on the skinny tire that isn't as good for drag racing as the taller wider tire. Plus the more tread the longer it will last in racing. There is also a point of diminishing returns. If your small block is making 300 hp you will go slower with full tubs and funny car tires because of their extra mass. If you are making 3000 hp then all that power has to be held with friction of the tires and you will make a ton of heat in those tires. Then there is the advantage of how those type of tires grow in diameter at speed giving you basically an change in gear ratio as you go down the track.

Anyway on a street car the difference in a 225 and a 265 tire will be almost 100% based on tread compound and nothing to do with size. Look at what size tire was the fastest 1/4 mile in this test
http://www.caranddriver.com/features/effects-of-upsized-wheels-and-tires-tested
Granted we are talking a 16 sec lightweight car but still, I'd love to see a similar test done on a SRT8. I do know that Ram SRT10's were hurt straight line with their monster tires compared to the more resonable tires that came on the Ford Lignting.