  One of the key questions in Astrophysics concerns the issue of whether there
exists an upper-mass limit to stars, and if so, what physical mechanism sets
this limit, which might also determine if the upper-mass limit is metallicity
(Z) dependent. We argue that mass loss by radiation-driven winds mediated by
line opacity is one of the prime candidates setting the upper-mass limit. We
present mass-loss predictions (dM/dt_wind) from Monte Carlo radiative transfer
models for relatively cool (Teff = 15kK) inflated very massive stars (VMS) with
large Eddington Gamma factors in the mass range 100-1000 Msun as a function of
metallicity down to 1/100 Z/Zsun. We employ a hydrodynamic version of our Monte
Carlo method, allowing us to predict the rate of mass loss (dM/dt_wind) and the
terminal wind velocity (vinf) simultaneously. Interestingly, we find wind
terminal velocities (vinf) that are low (100-500 km/s) over a wide Z-range, and
we propose that the slow winds from VMS are an important source of
self-enrichment in globular clusters. We also find mass-loss rates
(dM/dt_wind), exceeding the typical mass-accretion rate (dM/dt_accr) of 0.001
Msun/yr during massive-star formation. We express our mass-loss predictions as
a function of mass and Z, finding log dM/dt = -9.13 + 2.1 log(M/Msun) + 0.74
log(Z/Zsun) (Msun/yr). Even if stellar winds would not directly halt & reverse
mass accretion during star formation, if the most massive stars form by stellar
mergers stellar wind mass loss may dominate over the rate at which stellar
growth takes place. We therefore argue that the upper-mass limit is effectively
Z-dependent due to the nature of radiation-driven winds. This has dramatic
consequences for the most luminous supernovae, gamma-ray bursts, and other
black hole formation scenarios at different Cosmic epochs.
