Let $(\nu_{t})_{t\in{\mathbb{D}}^{*}}$ be a family of volume forms on a holomorphic family $X\to{\mathbb{D}}^{*}$ of compact complex manifolds, with analytic singularities at $t=0$. The asymptotic behavior of the total mass of $\nu_{t}$ is then given by

$$\nu_{t}(X_{t})\sim c|t|^{2\kappa_{\min}}(\log|t|^{-1})^{d}$$

with $c\in{\mathbb{R}}_{+}^{*}$, $\kappa_{\min}\in{\mathbb{Q}}$ and $d\in{\mathbb{N}}^{*}$, where $d\leq n:=\dim X_{t}$. Further, given any snc model ${\mathcal{X}}\to{\mathbb{D}}$ of $X\to{\mathbb{D}}^{*}$ such that $K_{X/{\mathbb{D}}^{*}}$ extends to a ${\mathbb{Q}}$-line bundle on ${\mathcal{L}}$ on ${\mathcal{X}}$ and $\psi$ extends to a continuous metric on ${\mathcal{L}}$, the rescaled measures

$$\mu_{t}:=\frac{\nu_{t}}{|t|^{2\kappa_{\min}}(2\pi\log|t|^{-1})^{d}},$$

viewed as measures on ${\mathcal{X}}^{\mathrm{hyb}}$, converge weakly to a Lebesgue type measure $\mu_{0}$ on a $d$-dimensional subcomplex $\Delta({\mathcal{L}})$ of $\Delta({\mathcal{X}})$.