  Quantum site percolation as a limiting case of binary alloy is studied
numerically in 2D within the tight-binding model. We address the transport
properties in all regimes - ballistic, diffusive (metallic), localized and
crossover between the latter two. Special attention is given to the region
close to the conduction band center, but even there the Anderson localization
persists, without signs of metal - insulator transition. We found standard
localization for sufficiently large samples. For smaller systems, novel partial
quantization of Landauer conductances, i. e. most values close to small
integers in arbitrary units is observed at band center. The crossover types of
conductance distributions (outside the band center) are found to be similar to
systems with corrugated surfaces. Universal conductance fluctuations in
metallic regime are shown to approach the known, theoretically predicted value.
The resonances in localized regime are Pendry necklaces. We tested Pendry's
conjecture on the probability of such rare conducting samples and it proved
consistent with our numerical results.
