  We study the vectorial length compactification of the space of conjugacy
classes of maximal representations of the fundamental group $\Gamma$ of a
closed hyperbolic surface $\Sigma$ in ${\rm PSL}(2,\mathbb R)^n$. We identify
the boundary with the sphere $\mathbb P((\mathcal{ML})^n)$, where
$\mathcal{ML}$ is the space of measured geodesic laminations on $\Sigma$. In
the case $n=2$, we give a geometric interpretation of the boundary as the space
of homothety classes of $\mathbb R^2$-mixed structures on $\Sigma$. We
associate to such a structure a dual tree-graded space endowed with an $\mathbb
R_+^2$-valued metric, which we show to be universal with respect to actions on
products of two $\mathbb R$-trees with the given length spectrum.
