This thesis presents an in-depth theoretical analysis of charge and spin transport properties
in complex forms of disordered graphene. It relies on innovative real space computational
methods of the time-dependent spreading of electronic wave packets. First a universal scaling
law of the elastic mean free path versus the average grain size is predicted for
polycrystalline morphologies and charge mobilities of up to 300.000 cm2 V.s are determined for
1 micron grain size while amorphous graphene membranes are shown to behave as Anderson
insulators. An unprecedented spin relaxation mechanism unique to graphene and driven by spin
pseudospin entanglement is then reported in the presence of weak spin-orbit interaction (gold
ad-atom impurities) together with the prediction of a crossover from a quantum spin Hall Effect
to spin Hall effect (for thallium ad-atoms) depending on the degree of surface ad-atom
segregation and the resulting island diameter.
