A simple two-dimensional (2D) model of a phase growing on a substrate
is introduced. The model is characterized by an adsorption rate q, and
a desorption rate p. It exhibits a wetting transition which may be vi
ewed as an unbinding transition of an interface from a wall. For p = 1
, the model may be mapped onto an exactly soluble equilibrium model ex
hibiting complete wetting with critical exponents gamma = 1/3 for the
diverging interface width and x(0) = 1 for the zero-level occupation.
For 0 < p not equal 1 a crossover to different exponents is observed w
hich is related to a Kardar-Parisi-Zhang-type nonlinearity.