the abovementioned transformation [@MN1; @MN2; @Review]. The bounded KPZ equation may experience, as parameters are varied, a phase transition from a depinned phase in which the interface escapes with probability one from the wall, to a pinned phase characterized by a finite expectation value of the stationary averaged height (measured from the wall). In the MN language ([*i.e.*]{} after employing the Cole-Hopf transformation) the pinning-depinning transition corresponds to a critical point separating an [*absorbing phase*]{} in which the order parameter goes exponentially to zero (depinned phase) to an [*active phase*]{} in which the order parameter takes a non-vanishing average value.

Surprisingly enough, it was shown a few years ago that the introduction of “upper” or “lower” walls into a given KPZ equation (with a fixed non-linearity sign) lead to quite different phenomenologies. The origin of this can be tracked down to the fact that the KPZ equation is not invariant upon inverting the height (see [@MN3] or [@Review] for a more detailed explanation). Taking, for instance, the sign of the coefficient of the KPZ non-linearity to be positive, the introduction of an upper wall leads to a (well established by now) set of critical exponents characterizing the, so called, multiplicative 