  The suppression of high transverse momentum P_T hadron production in
ultrarelativistic heavy-ion (A-A) collisions as compared to the scaled
expectation from proton-proton (p-p) collisions expressed as the nuclear
modification factor R_AA is experimentally well established and can be traced
back to interactions between the hard parton shower and the soft bulk matter.
Physical intuition suggests that the medium modification should cease to be
important when the hard scale of parton production is much larger than the
typical momentum scale in the medium (e.g. the temperature T) and that
consequently R_AA(P_T) -> 1 for P_T >> T. However, R_AA is not a 'simple'
observable, but rather results from many different mechanisms which influence
what happens when P_T increases. In particular, R_AA does not necessarily
approch unity even if the hadron momentum is probed at the kinematic limit of
the reaction. The aim of this work is to identify and discuss such mechanisms
and to present different model expectations of what one would find if one could
measure suppression out to the kinematic limit for hard hadron production and
give predictions for the P_T dependence at both RHIC and LHC.
