  We investigate the Kahler-Ricci flow on holomorphic fiber spaces whose
generic fiber is a Calabi-Yau manifold. We establish uniform metric convergence
to a metric on the base, away from the singular fibers, and show that the
rescaled metrics on the fibers converge to Ricci-flat Kahler metrics. This
strengthens previous work of Song-Tian and others. We obtain analogous results
for degenerations of Ricci-flat Kahler metrics.
