  The Lindblad dynamics of the XX quantum chain with large random fields $h_j$
(the couplings $J_j$ can be either uniform or random) is considered for
boundary-magnetization-drivings acting on the two end-spins. Since each
boundary-reservoir tends to impose its own magnetization, we first study the
relaxation spectrum in the presence of a single reservoir as a function of the
system size via some boundary-strong-disorder renormalization approach. The
non-equilibrium-steady-state in the presence of two reservoirs can be then
analyzed from the effective renormalized Linbladians associated to the two
reservoirs. The magnetization is found to follow a step profile, as found
previously in other localized chains. The strong disorder approach allows to
compute explicitly the location of the step of the magnetization profile and
the corresponding magnetization-current for each disordered sample in terms of
the random fields and couplings.
