How many amps can the 70mm, 90mm, and 105mm Hub Motors handle?

Each of these hub motors are measured by the watts they can handle vs. a definite amperage rating. 

Here are the ratings for each of the sets. (Rating per individual motor)

70mm: 350W
90mm: 500W
105mm: 500W

If you need to know how many amps they can handle you'll have to look at your batteries voltage. Here's the formula you can use to figure out how many amps each motor can handle/will pull from your ESC:

WATTS ÷ VOLTAGE = AMPERAGE

Remember, the number that you get here is for each motor by itself. Pushing your motors a bit beyond their capabilities is a common strategy (kind of like overclocking PC components), but remember that this can decrease the life of your motors over time or damage them if pushed too far). 

This information is really only relevant if you are using a VESC based ESC as the settings are entered in by the user. If you are using a basic ESC, like the ones we carry here on the MBoards site, the ESC handles all of this automatically.