  In this article, we consider a configuration of weighted random balls in
$\mathbb{R}^d$ generated according to a Poisson point process. The model
investigated exhibits inhomogeneity, as well as dependence between the centers
and the radii and heavy tails phenomena. We investigate the asymptotic behavior
of the total mass of the configuration of the balls at a macroscopic level.
Three different regimes appear depending on the intensity parameters and the
zooming factor. Among the three limiting fields, two are stable while the third
one is a Poisson integral bridging between the two stable regimes. For some
particular choices of the inhomogeneity function, the limiting fields exhibit
isotropy or self-similarity.
