  We prove that Calabi-Yau metrics on compact Calabi-Yau manifolds whose Kahler
classes shrink the fibers of a holomorphic fibration have a priori estimates of
all orders away from the singular fibers. This follows from a stronger
statement which gives an asymptotic expansion of these metrics as the fibers
shrink, in terms of explicit functions on the total space and with k-th order
remainders that satisfy uniform C^k-estimates with respect to a collapsing
family of background metrics.
