  We investigate to what extent the theory of N\'eron models of jacobians and
of abel-jacobi maps extends to relative curves over base schemes of dimension
greater than 1. We give a necessary and sufficient criterion for the existence
of a N\'eron model. We use this to show that, in general, N\'eron models do not
exist even after making a modification or even alteration of the base. On the
other hand, we show that N\'eron models do exist outside some codimension-2
locus.
