A model of deposition and growth in one dimension is studied in which
finite sized domains are deposited by the random sequential adsorption
process. The domains then grow with a time dependent growth rate. Whe
n the initial deposited domains are monomers and dimers the coverage i
s found exactly for a number of different growth rates. A continuum ve
rsion of this model is also considered. (C) 1998 Elsevier Science B.V.