What are the largest Technic-compatible tires on the market?
The largest wheels I know are these (I measured 110x63 mm, including tyres), but they are quite rare (only available in one single set):

Weels: 22969 "Wheel Technic Racing"
Tyres: 32298 "Tyre Power Puller"

The wheels itself are not that big, but if you include the tyres, they are really huge:



They would probably work really well for an RC car.