this universality class, give a firm evidence for the existence of a robust universality class. Contrarily to what previous simulations seemed to indicate [@MN3], our results are not a simple extension of the ones obtained for one-site, implying that spatial correlations play an important role. Table 1 gathers the values of the critical exponents in terms of $n$ for the two discrete models considered in this paper. From the Monte Carlo estimates, it cannot be discarded that they adopt the rational values $\beta_n=1/3$ and $\theta_n=2/9$, which combined with the exact values derived in [@MN1; @MN2], $\nu_\bot=1$ and $z=3/2$, would lead to $\beta_n/\nu_\bot= 1/3$. Note that our results do not compare well with those of the nonequilibrium wetting model reported in [@Haye2]. We believe this is probably due to the extremely long transients known to be present in that model. We have verified that the transition point is located at the same value of the control parameter for any value of the “attractiveness” parameter ($b$ in Model 1), either representing an attractive or a non attractive wall. For strong enough attractive walls, [*i.e.*]{} $b$ sufficiently negative, the transition becomes first order as in [@Haye2], while if the wall is weakly attractive 