Pierre Deligne in his celebrated paper entitling "[Local behavior of Hodge structures at infinity][1]" introduced  [Maximal degenerations][2] of Calabi-Yau manifolds. 

Let $\pi:X\to \mathbb C^*$ be a family of degeneration of of Calabi-Yau fibers. We have from [D. Barlet][3] asymptotic formula

$$\int_{X_s}\Omega_s\wedge\bar\Omega_s=C(\log |s|)^m|s|^{2k}(1+O(1))$$

for some $C \in \mathbb C^∗$, $k ∈ \mathbb Z, 0 \leq m \leq n = dim(X)$

We say that $X$ has [maximal degeneration][4] at $s = 0$,  if in the
formula above we have $m = n$.

Later this definition become very important in Miror symmetry for example in Siebert-Gross program or Kontsevich-Soibelman program.

>  I am woundring if there is any concrete example for maximal
> degeneration on moduli space of Calabi-Yau fibers. Moreover, which properties are known that central fiber $X_0$ must have , to get such maximal degeneration ?


  [1]: https://publications.ias.edu/sites/default/files/71_Localbehavior.pdf
  [2]: https://arxiv.org/pdf/math/0011041.pdf
  [3]: http://link.springer.com/article/10.1007/BF01394271
  [4]: http://www.alt.mathematik.uni-mainz.de/Members/ruddat/calabi-yau-degenerations-and-related-geometries