  We study the hopping transport of a quantum particle through finite, randomly
diluted percolation clusters in two dimensions. We investigate how the
transmission coefficient T behaves as a function of the energy E of the
particle, the occupation concentration p of the disordered cluster, the size of
the underlying lattice, and the type of connection chosen between the cluster
and the input and output leads. We investigate both the point-to-point contacts
and the busbar type of connection. For highly diluted clusters we find the
behavior of the transmission to be independent of the type of connection. As
the amount of dilution is decreased we find sharp variations in transmission.
These variations are the remnants of the resonances at the ordered,
zero-dilution, limit. For particles with energies within 0.25 <= E <= 1.75
(relative to the hopping integral) and with underlying square lattices of size
20x20, the configurations begin transmitting near p_a = 0.60 with T against p
curves following a common pattern as the amount of dilution is decreased. Near
p_b = 0.90 this pattern is broken and the transmission begins to vary with the
energy. In the asymptotic limit of very large clusters we find the systems to
be totally reflecting except when the amount of dilution is very low and when
the particle has energy close to a resonance value at the ordered limit or when
the particle has energy at the middle of the band.
