  Very massive stars (VMSs) formed via a sequence of stellar collisions in
dense star clusters have been proposed as the progenitors of massive black hole
seeds. VMSs could indeed collapse to form intermediate-mass black holes
(IMBHs), which would then grow by accretion to become the supermassive black
holes observed at the centers of galaxies and powering high-redshift quasars.
Previous studies have investigated how different cluster initial conditions
affect the formation of a VMS, including mass segregation, stellar collisions,
and binaries, among others. In this study, we investigate the growth of VMSs
with a new grid of Cluster Monte Carlo (CMC) star cluster simulations -- the
most expansive to date. The simulations span a wide range of initial
conditions, varying the number of stars, cluster density, stellar initial mass
function (IMF), and primordial binary fraction. We find a gradual shift in the
mass of the most massive collision product across the parameter space; in
particular, denser clusters born with top-heavy IMFs provide strong collisional
regimes that form VMSs with masses easily exceeding 1000 solar masses. Our
results are used to derive a fitting formula that can predict the typical mass
of a VMS formed as a function of the star cluster properties. Additionally, we
study the stochasticity of this process and derive a statistical distribution
for the mass of the VMS formed in one of our models, recomputing the model 50
times with different initial random seeds.
