We study the depinning transition for models representative of each of
the two universality classes of interface roughening with quenched di
sorder. For one of the universality classes, the roughness exponent ch
anges value at the transition, while the dynamical exponent remains un
changed. We also find that the prefactor of the width scales with the
driving force. We propose several scaling relations connecting the val
ues of the exponents on both sides of the transition, and discuss some
experimental results in light of these findings.