  We show that Lang's hyperbolic and function version conjectures hold for
surfaces $S$ of general type having a fibration of general type onto a curve
$C$. The notion of multiplicity used is natural, but not classical, which leds
to orbifold versions of Mordell's conjectures not reducible by ramified
covering tricks to the already solved cases. These are solved here in the two
above case (hyperbolic and function field cases). But the arithmetic case
(which follows from the abc conjecture) is left open. We also give an example
of a simply connected surface of general type having a fibration of general
type on $\Bbb P^1$, showing that the non-classical notion of multiplicity used
does not impose conditions on the fundamental group.
