Let $\pi\colon{\mathcal{X}}\to{\mathbb{D}}$ be an snc degeneration, ${\mathcal{L}}$ a ${\mathbb{Q}}$-line bundle on ${\mathcal{X}}$ extending $K_{X/{\mathbb{D}}^{*}}$, and $\psi$ a continuous metric on ${\mathcal{L}}$. Define $\kappa_{\min}$ as above, and set $d:=\dim\Delta({\mathcal{L}})$. Then, viewed as measures on ${\mathcal{X}}^{\mathrm{hyb}}$,

$$\mu_{t}:=\frac{\lambda(t)^{d}}{(2\pi)^{d}|t|^{2\kappa_{\min}}}e^{2\psi_{t}}$$

converges weakly to

$$\mu_{0}:=\sum_{\sigma}\left(\int_{Y_{\sigma}}\operatorname{Res}_{Y_{\sigma}}(\psi)\right)b_{\sigma}^{-1}\lambda_{\sigma},$$

where $\sigma$ ranges over the $d$-dimensional faces of $\Delta({\mathcal{L}})$. Here $\lambda_{\sigma}$ denotes normalized Lebesgue measure on $\sigma$ and $b_{\sigma}=\gcd_{i\in J}b_{i}$, where ${\mathcal{X}}_{0}=\sum_{i}b_{i}E_{i}$ and $E_{i}$, $i\in J$ are the divisors defining $\sigma$.