we are interested in the behaviour of ricci-flat kahler metrics on a compact calabi-yau manifold, with kahler classes approaching the boundary of the kahler cone. the case when the volume approaches zero is especially interesting since the corresponding complex monge-ampere equation degenerates in the limit. if the calabi-yau manifold is the total space of a holomorphic fibration, the ricci-flat metrics collapse to a metric the base, which `remembers' the fibration structure.