  We consider a recursively defined random set of points and its barycenter,
where the random set is constructed by the following inductive rule: Given a
realization of $n-1$ points, one of them is picked at random and serves as a
source the $n$-th point. We discuss the asymptotic behaviour of the barycentre
of this random set. The main analysis relies on the analsis of Hoppe trees, for
which we derive a limit theorem for the joint distribution of total length and
Wiener index.
