  We consider random sequential adsorption processes where the initially empty
sites of a graph are irreversibly occupied, in random order, either by monomers
which block neighboring sites, or by dimers. We also consider a process where
initially occupied sites annihilate their neighbors at random times. We verify
that these processes are well defined on infinite graphs, and derive forward
equations governing joint vacancy/occupation probabilities. Using these, we
derive exact formulae for occupation probabilities and pair correlations in
Bethe lattices. For the blocking and annihilation processes we also prove
positive correlations between sites an even distance apart, and for blocking we
derive rigorous lower bounds for the site occupation probability in lattices,
including a lower bound of 1/3 for Z^2. We also give normal approximation
results for the number of occupied sites in a large finite graph.
