  We study the charge and spin transport in a two terminal graphene nanoribbon
(GNR) decorated with random Gold (Au) adatoms using a Kane-Mele model. Two
commonly used GNRs, that is, the armchair graphene nanoribbon (AGNR) and the
zigzag graphene nanoribbon (ZGNR) are compared and contrasted, which shows that
in presence of Au adatoms, a somewhat robust $2e^2/h$ conductance plateau
occurs in the case of AGNR around the zero of the Fermi energy, while in ZGNR
this plateau is fragile. We show that this flat plateau, having a conductance
value $2e^2/h$, is not a hallmark signature of a topologically nontrivial
quantum spin Hall (QSH) state. Further the conductance decreases by a small
amount with the density of adatoms. On the other hand, the spin polarized
conductance shows distinct features of enhanced conductivity with increasing Au
adatom concentration. Further the fluctuations of the spin polarized
conductance have features that carry striking resemblance with the charge
conductance profile of the GNRs.
