RE: Stabilizers on control surfaces
You all missed the name for the extensions that are being referred to. I believe they are called aerodynamic balance tabs. Aerodynamic because, as Huber said, they reduce the load on the servo or the pilot's arms depending on what is moving the control.
Often they are used to hide weights that are called balance or anti flutter weights. Anything that can move the balance point of the surfaces towards the hinge line is a good thing.
On our models there really is no need for them. I have no idea why they are so popular with the 3D design crowd. Our servos easily have the power to move the surfaces and they don't put weights in them to assist with reducing flutter. So I have no idea why they use them. Style I guess.
And if you haven't figured it out from all this yet they do not have any stabilizing function. That is for the fixed surfaces as stated.