  This paper is a sequel to arXiv:1108.0967. We further study Gromov-Hausdorff
collapsing limits of Ricci-flat K\"ahler metrics on abelian fibered Calabi-Yau
manifolds. Firstly, we show that in the same setup as arXiv:1108.0967, if the
dimension of the base manifold is one, the limit metric space is homeomorphic
to the base manifold. Secondly, if the fibered Calabi-Yau manifolds are
Lagrangian fibrations of holomorphic symplectic manifolds, the metrics on the
regular parts of the limits are special K\"ahler metrics. By combining these
two results, we extend arXiv:math/0008018 to any fibered projective K3 surface
without any assumption on the type of singular fibers.
