Exact solution of a generalized model for surface deposition

We consider a model for surface deposition in one dimension, in the presence of both precursor-layer diffusion and desorption. The model is a generalization that includes random sequential adsorption (RSA), accelerated RSA, and growth-and-coalescence models as special cases. Exact solutions are obtained for the model for both its lattice and continuum versions. Expressions are obtained for physically important quantities such as the surface coverage, average island size, mass-adsorption efficiency, and the process efficiency. The connection between a limiting case of the model and epidemic models is discussed.