  The aim of our work is to study vertex-reinforced jump processes with
super-linear weight function $w(t) = t^\alpha$ , for some $\alpha>1$. On any
complete graph $G = (V, E)$, we prove that there is one vertex $v \in V$ such
that the total time spent at $v$ almost surely tends to infinity while the
total time spent at the remaining vertices is bounded.
