  We study the hopping transport of a quantum particle through randomly diluted
percolation clusters in two dimensions realized both on the square and
triangular lattices. We investigate the nature of localization of the particle
by calculating the transmission coefficient as a function of energy (-2 < E < 2
in units of the hopping integral in the tight-binding Hamiltonian) and
disorder, q (probability that a given site of the lattice is not available to
the particle). Our study based on finite size scaling suggests the existence of
delocalized states that depends on energy and amount of disorder present in the
system. For energies away from the band center (E = 0), delocalized states
appear only at low disorder (q < 15%). The transmission near the band center is
generally very small for any amount of disorder and therefore makes it
difficult to locate the transition to delocalized states if any, but our study
does indicate a behavior that is weaker than power-law localization. Apart from
this localization-delocalization transition, we also find the existence of two
different kinds of localization regimes depending on energy and amount of
disorder. For a given energy, states are exponentially localized for
sufficiently high disorder. As the disorder decreases, states first show
power-law localization before showing a delocalized behavior.
