in \[0,1\] and $a$ is a constant drift term analogous to that of (\[BKPZ\]).

2.  The configuration is changed to $h_{t+1}(x)=\min[h'_t(x\pm 1)+\gamma,h'_t(x)]$, where $\gamma$ is a constant whose precise value is not essential for the final results. We have set without loss of generality $\gamma=0.1$ as in previous numerical analyses.

3.  A hard wall at $h=0$ is introduced by way of the additional rule $h_t(x)=\min[h_t(x),0]$ [@MN3].

Finally, periodic boundary conditions are imposed and $h_t(x)$ is initially set to $0$.

The continuum counterpart of this model is known to be a KPZ equation [@krugs] with $\lambda<0$ in the presence of an upper wall [@note] which, as remarked before, is equivalent to the case $\lambda >0$ and a lower wall, and corresponds to the MN2 class. Numerical results for this model were first presented in [@MN3] and seemed to be consistent with mean-field ([*i.e.*]{} single-site) like behavior. However, a similar problem recently studied in the context of synchronization has revealed inconsistencies probably due to insufficient statistics [@Review; @synchro]. In this subsection improved simulation results are provided upon revisiting the analysis reported in [@MN3] for larger system sizes and longer sampling times. The case of an attractive wall, not included in [@MN3], is 