I think the answer is: It doesn't. If only one side of any differential has traction but the differential can bias the torque to move the vehicle - 100% of the torque is going to the side of the differential with resistance (traction in this case). The 50:50 split in the marketing material is really a (inarticulate) reference to the ratio of the gears driving the front and rear axles. They are often not the same. Often in RWD biased designs they'd be designed to send 70% or so of the torque to the rear axle. In FWD it would be reversed. The torque split value is relevant to how the car feels on dry pavement. In any other condition - the stated torque bias is basically meaningless.

There is also often a torque limit to one axle or the other. In the Lexus IS for example it's 30:70 Front:Rear in normal driving but can send as much as 50% to the front and IIRC 100% to the rear. What that means in real terms is that the design will only send 150 Ft/lbs forward if the rear tires have no traction. That could be both correctly stated as of the applied torque to the front and also correctly stated as 50% of the input torque being applied to the front. Both are correctly describing two different things using the same words that make it confusing. The torque limit is likely an inherent property of the center differential gear ratios and helical gear helix angle, not an electronic limit. It's designed so that the maximum force applied to the front is half of input torque due to a friction limit in the engineering of the helical mesh.

In the case of the IS awd - if you were on dry pavement full throttle and the engine has 300 ft lbs of torque (it's a lot more due to transmission gearing, but I'm ignoring that for now), 100 ft lbs goes to the front, 200 goes to the rear. If the rear is on rollers, 100% goes to the front, but it would not exceed 150 ft lbs of torque going to the front. So, it would be both 100% relative to the torque out of the transfer case, but 50% relative to the input.