  Nominally identical materials exchange net electric charge during contact
through a mechanism that is still debated. `Mosaic models', in which surfaces
are presumed to consist of a random patchwork of microscopic donor/acceptor
sites, offer an appealing explanation for this phenomenon. However, recent
experiments have shown that global differences persist even between
same-material samples, which the standard mosaic framework does not account
for. Here, we expand the mosaic framework by incorporating global differences
in the densities of donor/acceptor sites. We develop an analytical model,
backed by numerical simulations, that smoothly connects the global and
deterministic charge transfer of different materials to the local and
stochastic mosaic picture normally associated with identical materials. Going
further, we extend our model to explain the effect of contact asymmetries
during sliding, providing a plausible explanation for reversal of charging sign
that has been observed experimentally.
