  The centres of galaxies host nuclear stellar clusters, supermassive black
holes, or both. The origin of this dichotomy is still a mystery. Nuclear
stellar clusters are the densest stellar system in the Universe, so they are
ideal places for runaway collisions to occur. Previous studies have proposed
the possible existence of a critical mass scale in such clusters, for which the
occurrence of collisions becomes very frequent and leads to the formation of a
very massive object. While it is difficult to directly probe this scenario with
simulations, we here aim for a proof of concept using toy models where the
occurrence of such a transition is shown based on simplified compact systems,
where the typical evolution time-scales will be faster compared to the real
Universe. Indeed our simulations confirm that such a transition takes place and
that up to 50 per cent of the cluster mass can go into the formation of a
central massive object for clusters that are above the critical mass scale. Our
results thus support the proposed new scenario on the basis of idealized
simulations. A preliminary analysis of observed nuclear star clusters shows
similar trends related to the critical mass as in our simulations. We further
discuss the caveats for the application of the proposed scenario in real
nuclear star clusters.
