ABS works by monitoring sensors only measuring the speed of rotation of each wheel. If one wheel begins rotating at a much slower speed then the rest, the ABS will begin to rapidly(somewhere in the neighborhood of 60 times a second) release and apply the brakes. Therefore, regardless of overall diameter, AS LONG AS ALL 4 WHEELS have the same overall diameter, it will NOT effect ABS performance. However, a larger wheel typically weighs more and therefore has a greater rotational inertia than a smaller wheel. This will reduce overall braking effectiveness. And when you start to run a much larger than stock diameter tire you will reduce the overall braking performance of the car further due to the larger force(wheel diameter) acting in the opposite direction of braking force(rotor diameter). Just think of a lever, if you move the fulcrum farther from the intended movement, the harder it is to move the lever. I hope this makes sense.
In higher end cars with stability control, a change in diameter can have a significant effect because those systems measure much more than the rotational speed of the wheels (such as yaw, roll, steering angle, throttle position, etc.) to determining what action should be taken to help stabilize the car. Therefore, by changing the input of a single variable, the wheel diameter, and not changing the inputs of the rest of the sensors or changing the program that does the calculations, you upset the whole system.
