  We consider weighted random balls in $\real^d$ distributed according to a
random Poisson measure with heavy-tailed intensity and study the asymptotic
behaviour of the total weight of some configurations in $\real^d$. This
procedure amounts to be very rich and several regimes appear in the limit,
depending on the intensity of the balls, the zooming factor, the tail
parameters of the radii and of the weights. Statistical properties of the limit
fields are also evidenced, such as isotropy, self-similarity or dependence. One
regime is of particular interest and yields $\alpha$-stable stationary
isotropic self-similar generalized random fields which recovers Takenaka
fields, Telecom process or fractional Brownian motion.
