  We consider a collection of Euclidean random balls in ${\Bbb R}^d$ generated
by a determinantal point process inducing interaction into the balls. We study
this model at a macros\-copic level obtained by a zooming-out and three
different regimes --Gaussian, Poissonian and stable-- are exhibited as in the
Poissonian model without interaction. This shows that the macroscopic behaviour
erases the interactions induced by the determinantal point process.
