  In this paper, we consider a cluster model of weighted Euclidean random balls
generated by a shot-noise Cox process. It is an example of cluster point
process. We perform a scaling on the model by shrinking the radii of the balls
and compensate this effect by increasing the (mean) number of balls in each
cluster, or/and increasing the (mean) number of clusters. We consider two
different scenarios, say a local and a global scenarios. Heuristically, in the
first scenario, we focus on the mean number of large balls in a cluster while
in the second one, we focus on the global mean number of large balls in the
model. According to the different scenarios, the cluster structure can persist
at the limit or disappear.
