On the shape of the domain occupied by a supercritical branching random walk

A particle system on ^d is considered whose evolution is as follows. At each unit of time each particle independently is replaced by a new generation. The size of a new generation descending from a particle at site x has a distribution and each of its members independently jump to a neighbouring site with probability 1/2d. Let (T) be the set of the occupied sites at time T. The geometrical properties of (T) are studied.