  We show that pure spin Hall current, flowing out of a four-terminal
phase-coherent two-dimensional electron gas (2DEG) within inversion asymmetric
semiconductor heterostructure, contains contributions from both the extrinsic
mechanisms (spin-orbit dependent scattering off impurities) and the intrinsic
ones (due to the Rashba coupling). While the extrinsic contribution vanishes in
the weakly and strongly disordered limits, and the intrinsic one dominates in
the quasiballistic limit, in the crossover transport regime the spin Hall
conductance, exhibiting sample-to-sample large fluctuations and sign change, is
not simply reducible to either of the two mechanisms, which can be relevant for
interpretation of experiments on dirty 2DEGs [V. Sih et al., Nature Phys. 1, 31
(2005)].
