Dimensions of supercritical branching processes in varying environments

Let [not partial differential][Gamma] be the boundary of a family tree [Gamma] associated with a supercritical branching process in varying environments. In this paper, the Hausdorff dimension, the upper box dimension and the packing dimension of [not partial differential][Gamma] are computed explicitly. In contrast to the (fixed environment) Galton-Watson case, the Hausdorff and upper box dimension may take different values.