...or the engine powers the front-right wheel or left-rear or two of the four, whichever has the least traction at the moment...
...just 'cause she cooks one wheel don't mean the power always goes there, the classic case of the stuck truck on a boat ramp. First, truck gets stuck. Right Rear wheel just goes werrrrrrrrrrrrrrrrrrrrrrrrrr and smokes and burns up. So, four guys get in the truck bed. They lean right, and, surprise, now its the left rear wheel! SO they rock back and forth, and the wheel that loses traction is the one with the least weight, which changes when the guys shift their weights. Finally, the guys get desperate and start jumping like monkeys on a bed, which doesn't help much other than to make the truck go up and down and the tire tries to dig in but the other one picks up instead. Finally, after half an hour, the truck gains traction from the puddle of rubber that's laid down on the slick ramp and gets going.
Now in AWD it depends on the diffs. You can have an AWD with open diffs (all power to the path of least resistance) which will give you four times the problems with traction (any 1 wheel will slip and get 100% power) as opposed to something like a serious AWD used in rally cars, which have Limited-Slip diffs front, center and rear. They can spin all four wheels, but not really on the road because of all the grip.
Now you ask, why open diffs if they get that bad of a traction? Answer: Saves $$$! Better gas mileage, cheap to make, and a little less wear on the tires.