What affect does the horizontal stab position have aerodynamically if it is located above the thrust line, on the thrust line or below the thrust line?

The only thing to really avoid is having the horizontal stab exactly in line with the wing - can cause some really strange handling, when the stab can't decide which side of the wing vortex stream to stick to. Horizontal stab positioned well above the wing, as with a T tail can cause some wild flat spins that may be hard to recover from, since the stab gets well blanked by the wing. Otherwise, I would expect no problem either way.

The horizontal stab is in the downwash from the wing, so when the wing is lifting, the stab is at a relative angle of attack(negative) to its physical angle, and generates a downward force. this force will change with the amount of lift being generated by the wing

So a high stab is better, but not to high.
Flap deployment can cause all sorts of strange effects.
All this will be compounded by a sensitive CG position.
Bob

Like so many other things, it depends on the mission for which the aircraft is being designed. For a 3D airplane (and many aerobatic ones), the most common setup is to have the thrust line, the wing and the elevator all in a line. The reason for this is twofold. Such a setup provides the same response right side up, or upside down, and it places the elevator central in the prop blast so that control when hovering is symmetrical.

“T” tails became popular with such rear engine transports as the B-727 and the DC-9 where the main reason was to get the horizontal stabilizer away from the engines. Though that configuration was also used on the Lockheed C-141, and the C-5, I always suspect it was more of a style thing than an engineering solution. The advent of the “T” tail brought with it something called a super stall where at high pitch angles, the tail is blanketed by the wing and the aircraft will continue to pitch up in spite of elevator input. I notice that the present generation of transport aircraft have gone back to a more conventional tail configuration.

A “T” tail was used on a couple of general aviation airplanes, particularly the Beech Skipper, and the Piper Tomahawk. I instructed for about a year in a Tomahawk (and have quite a few hours flying a Skipper), and while they don’t have a problem with “super stall’, elevator control is not as positive when landing as other training aircraft I have flown.

Outside these considerations, any other location will be OK. I like to keep the horizontal stabilizer in the prop blast because it gives better control, but for a typical sport model, whether it is above or below the wing, or the thrust line doesn’t seem to make very much difference.