  We consider a model for random deposition of monomers on a line with
extrinsic precursor states. As the adsorbate coverage increases, the system
develops non-trivial correlations due to the diffusion mediated deposition
mechanism. In a numeric simulation, we study various quantities describing the
evolution of the island structure. We propose a simple, self-consistent theory
which incorporates pair correlations. The results for the correlations, island
density number, average island size and probabilities of island nucleation,
growth and coagulation show good agreement with the simulation data.
