  In 1981, J. Hawkes conjectured the exact form of the Hausdorff gauge function
for the boundary of supercritical Galton-Watson trees under a certain
assumption on the tail at the infinity of the total mass of the branching
measure. Hawkes's conjecture has been proved by T. Watanabe in 2007 as well as
other other precise results on fractal properties of the boundary of
Galton-Watson trees. The goal of this paper is to provide an elementary proof
of Hawkes's conjecture under a less restrictive assumption than in T.
Watanabe's paper, by use of size-biased Galton-Watson trees introduced by
Lyons, Pemantle and Peres in 1995.
