extensively studied, specially after its connections with non-equilibrium wetting [@Haye1; @Haye2; @Lisboa] and with the problem of synchronization in extended systems were established [@synchro; @Review], the MN2 class remains poorly studied. Furthermore, recent numerical analysis have revealed that the preliminary critical exponent values reported in [@Hwa] might be far from their true asymptotic values.

Aimed at clarifying these issues it is the purpose of this paper to analyze the MN2 phase transition in one dimensional systems using: i) mean-field and field-theoretical techniques and ii) numerical (Monte Carlo) analysis of different models claimed to belong to this class.

Finally let us stress that if the wall becomes attractive, rather than simply bounding, new phenomenology might appear. This is particularly interesting in the context of synchronization [@Review; @synchro]. This possibility will also be discussed along the paper.

The MN2 class
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Let us consider a KPZ equation with a positive non-linearity coefficient, $\lambda >0$, in the presence of a lower wall, $$\partial_t h(x,t) = a + b ~e^{-ph} + D \nabla^2 h + \lambda (\nabla h)^2
+ \sigma \eta(x,t).
\label{BKPZ}$$ where $h$ is a height variable, $a$ represents a constant drift while $ b ~e^{-ph}$ is a bounding wall. The parameter $p>0$ 