  In limited mobility (LM) models of thin film deposition, the final position
of each atom or molecule is chosen according to a set of stochastic rules
before the incidence of another atom or molecule. Here we investigate the
possibility of a LM model to reproduce features of a more realistic approach
that represents the interplay of collective adatom diffusion and the external
flux. In the LM model introduced here, each adatom may execute $G$ hops to
neighboring columns of the deposit, but a hop attempt from a site with $n$
lateral neighbors has probability $P^n$, with $P<1$. These rules resemble those
of the Clarke-Vvedensky (CV) model without energy barriers at step edges, whose
main parameters are the diffusion-to-deposition ratio $R$ on terraces and the
detachment probability $\epsilon$ per lateral neighbor. At short times, the
roughness of the LM model can be written in terms of a scaling function of $G$
and $P$ and the growth exponent is consistent with the Villain-Lai-Das Sarma
universality class. The evolution of the surface roughness and of the
autocorrelation function of the CV model is reproduced with reasonable accuracy
by the LM model with suitable choices of parameters. The increase of the
parameters $G$ and $R$ of those models produces smoother film surfaces, while
the increase of $P$ and $\epsilon$ smoothen the terrace boundaries at short
lengthscales. However, the detachment probabilities of the two models have very
different effects on the surface roughness: in the LM model, for fixed $G$, the
surface roughness increases as $P$ increases; in the CV model, the surface
smoothens as $\epsilon$ increases, for fixed $R$. This result is related to the
non-Markovian nature of the LM model, since the diffusivity of an adatom
depends on its history at the film surface and may be severely reduced after a
detachment from a terrace step.
