PARSEC evolutionary tracks of massive stars up to 350 Msun at metallicities 0.0001 <= Z <= 0.04

We complement the. parsec data base of stellar evolutionary tracks with new models of massive stars, from the pre-main-sequence phase to the central carbon ignition. We consider a broad range of metallicities, 0.0001 ≤ Z ≤ 0.04 and initial masses up to Mini = 350 M⊙. The main difference with respect to our previous models of massive stars is the adoption of a recent formalizm accounting for the mass-loss enhancement when the ratio of the stellar to the Eddington luminosity, Λe, approaches unity. With this new formalizm, the models are able to reproduce the Humphreys-Davidson limit observed in the Galactic and Large Magellanic Cloud colour-magnitude diagrams, without an ad hoc mass-loss enhancement. We also follow the predictions of recent wind models indicating that the metallicity dependence of the mass-loss rates becomes shallower when Λe approaches unity. We thus find that the more massive stars may suffer from substantial mass-loss even at low metallicity. We also predict that the Humphreys-Davidson limit should become brighter at decreasing metallicity. We supplement the evolutionary tracks with new tables of theoretical bolometric corrections, useful to compare tracks and isochrones with the observations. For this purpose, we homogenize existing stellar atmosphere libraries of hot and cool stars (Potsdam Wolf-Rayet, ATLAS9 and PHOENIX) and we add, where needed, new atmosphere models computed with. wm-basic. The mass, age and metallicity grids are fully adequate to perform detailed investigations of the properties of very young stellar systems, both in local and distant galaxies. The new tracks supersede the previous old. padova models of massive stars.