  We present a new study of the collisional runaway scenario to form an
intermediate-mass black hole (IMBH, MBH > 100 Msun) at the centre of a young,
compact stellar cluster. The first phase is the formation of a very dense
central core of massive stars (Mstar =~ 30-120 Msun) through mass segregation
and gravothermal collapse. Previous work established the conditions for this to
happen before the massive stars evolve off the main sequence (MS). In this and
a companion paper, we investigate the next stage by implementing direct
collisions between stars. Using a Monte Carlo stellar dynamics code, we follow
the core collapse and subsequent collisional phase in more than 100 models with
varying cluster mass, size, and initial concentration. Collisions are treated
either as ideal, ``sticky-sphere'' mergers or using realistic prescriptions
derived from 3-D hydrodynamics computations. In all cases for which the core
collapse happens in less than the MS lifetime of massive stars (~3 Myr), we
obtain the growth of a single very massive star (VMS, Mstar =~ 400-4000 Msun)
through a runaway sequence of mergers. Mass loss from collisions, even for
velocity dispersions as high as sigma1D ~ 1000 km/s, does not prevent the
runaway. The region of cluster parameter space leading to runaway is even more
extended than predicted in previous work because, in clusters with sigma1D >
300 km/s, collisions accelerate (and, in extreme cases, drive) core collapse.
Although the VMS grows rapidly to > 1000 Msun in models exhibiting runaway, we
cannot predict accurately its final mass. This is because the termination of
the runaway process must eventually be determined by a complex interplay
between stellar dynamics, hydrodynamics, and the stellar evolution of the VMS.
[abridged]
