We consider a percolation model on the d-dimensional Euclidean space (d ≧ 2) which consists of spheres centred at the points of a Poisson point process of intensity λ. The radii of the spheres are random and are chosen independently and identically according to a distribution of a positive random variable. We show that the percolation function is continuous everywhere except perhaps at the critical point. Further, we show that the percolation functions converge to the appropriate percolation function except at the critical point when the radius random variables are uniformly bounded and converge weakly to another bounded random variable.
