We have established under which conditions core collapse of a spherical cluster occurs before massive stars have time to evolve off the main sequence (MS). We consider cluster central velocity dispersions of 100 km s(-1) and higher, appropriate for galactic nuclei. At such high velocities, binary stars play little dynamical role and are therefore neglected. On the other hand whether collisions allow the growth of very massive stars (VMS, with M-* >> 100 M-circle dot) or, on the contrary, grind them down is a central unknown addressed in this work. We find that, in spite of the high relative velocities, run-away growth of a VMS, a likely progenitor for an intermediate-mass BH (IMBH), occurs in all clusters with short enough a core collapse time.