We study the stochastic dynamics of deposition-evaporation cooperative
processes of dimers, trimers, etc., in two- and higher-dimensional la
ttices. The dimer system in bipartite lattices allows for an exact sol
ution of dynamic correlations and scaling functions by means of a quan
tum spin equivalence. Autocorrelations exhibit a diffusive asymptotic
kinetics and crossovers of different dynamic regimes in highly anisotr
opic lattices. Monte Carlo simulations combined with finite-size scali
ng arguments support the validity of the diffusive picture in more gen
eral situations. Steady-state coverages and diffusion constants are ob
tained using mean-field approaches, spin wave calculations, and random
walk analyses in nearly jammed configurations.