  We solve exactly a special case of the anisotropic directed bond percolation
problem in three dimensions, in which the occupation probability is 1 along two
spatial directions, by mapping it to a five-vertex model. We determine the
asymptotic shape of the ininite cluster and hence the direction dependent
critical probability. The exponents characterising the fluctuations of the
boundary of the wetted cluster in d-dimensions are related to those of the
(d-2)-dimensional KPZ equation.
