Let $\pi\colon X\to{\mathbb{D}}^{*}$ be a holomorphic family of Calabi-Yau Kähler manifolds $X_{t}$, meromorphic at $t=0$, and let $\mu_{t}$ be the corresponding family of canonical probability measures. For any snc model ${\mathcal{X}}$, $\mu_{t}$ converges in ${\mathcal{X}}^{\mathrm{hyb}}$ to a skeletal measure $\mu_{0}$ supported in $\Delta({\mathcal{X}})$.