  We study a $d=2$ discrete solid--on--solid model of complete wetting of a
rough substrate with random self--affine boundary, having roughness exponent
$\zeta_s$. A suitable transfer matrix approach allows to discuss adsorption
isotherms, as well as geometrical and thermal fluctuations of the interface.
For $\zeta_s\leq 1/2$ the same wetting exponent $\psi=1/3$ as for flat
substrate is obtained for the dependence of the coverage, $\theta$, on the
chemical potential, $h$ ($\theta\sim h^{-\psi}$ for $h\to 0$). The expected
existence of a zero temperature fixed point, leading to $\psi=\zeta_s
/(2-\zeta_s)$ for $\zeta_s>1/2$, is verified numerically in spite of an
unexpected, very slow convergence to asymptotics.
