As a canonical model for wetting far from thermal equilibrium we study a
Kardar-Parisi-Zhang interface growing on top of a hard-core substrate.
Depending on the average growth velocity the model exhibits a non-equilibrium
wetting transition which is characterized by an additional surface critical
exponent theta. Simulating the single-step model in one spatial dimension we
provide accurate numerical estimates for theta and investigate the distribution
of contact points between the substrate and the interface as a function of
time. Moreover, we study the influence of finite-size effects, in particular
the time needed until a finite substrate is completely covered by the wetting
layer for the first time.Comment: 17 pages, 8 figures, revisio