We study spin transport through graphene-like substrates in the presence of one or several, locally induced spin-orbit coupling (SOC) terms resulting from periodically placed strips, on their top and decorated with a random distribution of impurities. Intrinsic SOC (ISOC), Rashba SOC (RSOC) and/or pseudo-spin-inversion-asymmetry coupling (PIAC) are considered. A systematic investigation of the spin conductance identifies the main SOC terms which lead to its energy dependence as well as the extent to which the impurity concentration and each SOC term can affect it. In addition, the spin current flow is considered in the presence of different SOC& #xD; impurities and their related group symmetry such C6v , C3v , D6h and D3h . Further, we show that the quantum spin-Hall effect (QSHE) related to the spin edge states depends only on the spin character when the PIA and ISO terms are not sublattice resolved, and on both the spin and sublattice character when they are. In addition, we show that the RSO term plays a major role in obtaining edge states that are either protected on both edges or only& #xD; on one edge against backscattering. This Rashba term creates an anticrosing gap that affects the symmetry in& #xD; the edge localizations and leads to half-topological states. The results can facilitate the experimental choice of appropriately decorated strips to (i) develop spin-transistor devices by tuning the Fermi energy, (ii) control the robustness of the QSHE against backscattering even in the presence of on-site sublattice asymmetry induced by a transverse electric field or functionalizations, and (iii) provide a strong theoretical support for spintronic devices.
