I am highly entertained by the discussion on axial forces on the three-rotor system of the Trent.
Having done the analysis a time or two on various engines, let me state some basic truths:
1) the compressor (or fan) rotor is always pulling forward.
2) the turbine rotor is always pulling aft.
3) there is no way one can tell, by inspection, which of these two forces is the greater. It's analogous to two teams of elephants in a tug-of-war.
In fact, the net load on the thrust bearing may be forward at one operating condition, and aft at some other condition. If such a crossover occurs, it's less than desirable; it causes chatter in the lightly-loaded thrust bearing. Designers will make every effort to move the crossover to some sub-idle point.