  Drmota and Gittenberger (1997) proved a conjecture due to Aldous (1991) on
the height profile of a Galton-Watson tree with an offspring distribution of
finite variance, conditioned on a total size of $n$ individuals. The conjecture
states that in distribution its shape, more precisely its scaled height profile
coincides asymptotically with the local time process of a Brownian excursion of
duration 1. We give a proof of the result, which extends to the case of an
infinite variance offspring distribution. This requires a different strategy,
since in the infinite variance case there is no longer a relationship to the
local time of Brownian resp. L\'{e}vy excursions.
