If carrying a three person tent when backpacking, what's the recommended way to split it up so that the weight is balanced out among all three people going?
Generally I find a three person tent small and light enough that you don't need to split it up when backpacking - indeed I find it's much less hassle to keep it all in one place so when you come to put it up, you know exactly where everything is.
Instead, I'd advocate balancing the weight via other means - distributing food differently is probably the easiest, but this could work with anything else you're carrying (cooking equipment, clothes, etc.)
If you must split the tent up, then I'd move the poles and pegs into a separate bag and put that in another pack (but personally I'd make sure you keep them together.)
I'm assuming there won't be three parts of equal weight. Depending on the tent design, you could be talking main room, fly, and poles. You could break it into threes that way, then swap other items to equalize the load. So, if you're carrying the main room, perhaps someone could carry some of your share of the food, for example.