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  1. ABSTRACT Evolved Wolf–Rayet stars form a key aspect of massive star evolution, and their strong outflows determine their final fates. In this study, we calculate grids of stellar models for a wide range of initial masses at five metallicities (ranging from solar down to just 2 per cent solar). We compare a recent hydrodynamically consistent wind prescription with two earlier frequently used wind recipes in stellar evolution and population synthesis modelling, and we present the ranges of maximum final masses at core He-exhaustion for each wind prescription and metallicity Z. Our model grids reveal qualitative differences in mass-loss behaviour of the wind prescriptions in terms of ‘convergence’. Using the prescription from Nugis & Lamers the maximum stellar black hole is found to converge to a value of 20–30 M⊙, independent of host metallicity; however, when utilizing the new physically motivated prescription from Sander & Vink there is no convergence to a maximum black hole mass value. The final mass is simply larger for larger initial He-star mass, which implies that the upper black hole limit for He-stars below the pair-instability gap is set by prior evolution with mass loss, or the pair instability itself. Quantitatively, we find the critical Z for pair-instability (ZPI) tomore »be as high as 50 per cent Z⊙, corresponding to the host metallicity of the Large Magellanic Cloud. Moreover, while the Nugis & Lamers prescription would not predict any black holes above the approx 130 M⊙ pair-instability limit, with Sander & Vink winds included, we demonstrate a potential channel for very massive helium stars to form such massive black holes at ∼2 per cent Z⊙ or below.« less