  Some studies have claimed a universal stellar upper-mass limit of 150 Msun. A
factor that is often overlooked is that there might be a difference between the
current and initial masses of the most massive stars, as a result of mass loss.
We present Monte Carlo mass-loss predictions for very massive stars in the
range 40-300 Msun, with large luminosities and Eddington factors Gamma. Using
our new dynamical approach, we find an upturn in the mass-loss vs. Gamma
dependence, at the point where the winds become optically thick. This coincides
with the location where wind efficiency numbers surpass the single-scattering
limit of Eta = 1, reaching values up to Eta = 2.5. Our modelling suggests a
transition from common O-type winds to Wolf-Rayet characteristics at the point
where the winds become optically thick. This transitional behaviour is also
revealed with respect to the wind acceleration parameter beta, which starts at
values below 1 for the optically thin O-stars, and naturally reaches values as
high as 1.5-2 for the optically thick Wolf-Rayet models. An additional finding
concerns the transition in spectral morphology of the Of and WN characteristic
He II line at 4686 Angstrom. When we express our mass-loss predictions as a
function of the electron scattering Gamma_e (=L/M) only, we obtain a mass-loss
Gamma dependence that is consistent with a previously reported power-law Mdot
propto Gamma^5 (Vink 2006) that was based on our semi-empirical modelling
approach. When we express Mdot in terms of both Gamma and stellar mass, we find
Mdot propto M^0.8 Gamma^4.8 for our high Gamma models. Finally, we confirm that
the Gamma-effect on the mass-loss predictions is much stronger than that of an
increased helium abundance, calling for a fundamental revision in the way mass
loss is incorporated in evolutionary models of the most massive stars.
