Using Monte Carlo codes, we follow the collisional evolution of clusters in a variety of scenarios. We consider the conditions under which a cluster of main-sequence stars may undergo rapid core collapse due to mass segregation, thus entering a phase of runaway collisions, forming a very massive star (VMS, M-* > 1000M(circle dot)) through repeated collisions between single stars. Although collisional mass loss is accounted for realistically, we find that a VMS forms even in proto-galactic nuclei models with a high velocity dispersion (many 100 km s(-1)). Such a VMS may be a progenitor for an intermediate-mass black hole (M-center dot >= 100 M-circle dot). In contrast, in galactic nuclei hosting a central massive black hole, collisions are found to be disruptive. The stars which are subject to collisions are progressively ground down by high-velocity collisions and a merger sequence appears impossible.