  We study polarised degenerations of $n$-dimensional Calabi-Yau hypersurfaces
$\{ F_0F_1\ldots F_m+tF=0\} $, where the essential skeleton has dimension
$1\leq m\leq n-1$. We will describe the limiting behaviour of the Calabi-Yau
potential at the $C^0$-level, in terms of an optimal transport problem, and in
terms of non-archimedean potential theory.
