  The theoretical description of transport in a wide class of novel materials
is based upon quantum percolation and related random resistor network (RRN)
models. We examine the localization properties of electronic states of diverse
two-dimensional quantum percolation models using exact diagonalization in
combination with kernel polynomial expansion techniques. Employing the local
distribution approach we determine the arithmetically and geometrically
averaged densities of states in order to distinguish extended, current carrying
states from localized ones. To get further insight into the nature of
eigenstates of RRN models we analyze the probability distribution of the local
density of states in the whole parameter and energy range. For a recently
proposed RRN representation of graphene sheets we discuss leakage effects.
