  The Weibull function is widely used to describe skew distributions observed
in nature. However, the origin of this ubiquity is not always obvious to
explain. In the present paper, we consider the well-known Galton-Watson
branching process describing simple replicative systems. The shape of the
resulting distribution, about which little has been known, is found essentially
indistinguishable from the Weibull form in a wide range of the branching
parameter; this can be seen from the exact series expansion for the cumulative
distribution, which takes a universal form. We also find that the branching
process can be mapped into a process of aggregation of clusters. In the
branching and aggregation process, the number of events considered for
branching and aggregation grows cumulatively in time, whereas, for the binomial
distribution, an independent event occurs at each time with a given success
probability.
