  We study from a geographical point of view fibrations of threefolds over
smooth curves, such that the general fibre is of general type. We prove the
non-negativity of certain relative invariants under general hypotheses and give
lower bounds for the self-interssection of the relative canonical divisor of
the fibration, depending on other relative invariants. We also study the
influence of the relative irregularity on these bounds. A more detailed study
of the lowest cases of the bounds is given.
