HaHa, I think this was the question that got me into the forums a looong time ago. Like you, I thought "this is a big battlefield some 30 miles wide by 15 deep; I want the THawk to re-position my troops" and was effectively told the same thing - wherupon I started to work out all sorts of ways of achieving it.
During a turn, Air transports can bring stuff in to the battlefield, or evacuate it off table. Although you can remain on the table (see below), generally air transports are better off leaving the table at the end of the turn during the end phase. However, there are a couple of ways to keep the air transport full so that it can effectively be moving stuff around in the way that you envisage (though in practice it is not that easy to pull off).

Whilst the air-transport is on the ground, it becomes a "ground unit" for all purposes, except that it may 'disengage' in the end-phase; this is the *only* way it can fly off!
If it remains on the table at the end of a turn, the following turn it activates like any other ground formation using the standard activations (*not* the aircraft activations). So it has a ground unit move of 0 cms, can shoot and assault etc - and can be "broken" if BMs become excessive. Note, it *may* disengage when broken, whereupon it leaves the table with twice its DC in BMs.
I hope that makes things clearer
