A discussion of epitaxial growth is presented for those situations (OMVPE,
CBE, ALE, MOMBE, GSMBE, etc.) when the kinetics of surface processes associated
with molecular precursors may be rate limiting. Emphasis is placed on the
identification of various {\it characteristic length scales} associated with
the surface processes. Study of the relative magnitudes of these lengths
permits one to identify regimes of qualitatively different growth kinetics as a
function of temperature and deposition flux. The approach is illustrated with a
simple model which takes account of deposition, diffusion, desorption,
dissociation, and step incorporation of a single precursor species, as well as
the usual processes of atomic diffusion and step incorporation. Experimental
implications are discussed in some detail.