At time t=0 we have a Poisson random field on d. Each particle executes a critical branching Wiener process starting from its position at time t=0. Let RT be the radius of the largest ball around the origin of d which does not contain any particle at time T. Our goal is to characterize the properties of the stochastic process {RT,T0}.This article is dedicated to the memory of Professor Roland L. Dobrushin.