  We study, using noise reduction techniques, layer by layer epitaxial growth
in limited mobility solid-on-solid nonequilibrium surface growth models, which
have been introduced in the context of kinetic surface roughening in ideal
molecular beam epitaxy. Multiple hit noise reduction and long surface diffusion
length lead to qualitatively similar layer by layer epitaxy in 1+1 and 2+1
dimensional limited mobility growth simulations. We discuss the dynamic scaling
characteristics connecting the transient layer by layer growth regime with the
asymptotic kinetically rough growth regime.
