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We complement the PARSEC data base of stellar evolutionary tracks with newmodels of massive stars, from the pre-main sequence phase to the central carbonignition. We consider a broad range of metallicities, 0.0001$\leq Z \leq$0.04and initial masses up to $M_{\rm ini}=350\,M_\odot$. The main difference withrespect to our previous models of massive stars is the adoption of a recentformalism accounting for the mass-loss enhancement when the ratio of thestellar to the Eddington luminosity, $\Gamma_e$, approaches unity. With thisnew formalism, the models are able to reproduce the Humphreys-Davidson limitobserved in the Galactic and Large Magellanic Cloud colour-magnitude diagrams,without an ad hoc mass-loss enhancement. We also follow the predictions ofrecent wind models indicating that the metallicity dependence of the mass-lossrates becomes shallower when $\Gamma_e$ approaches unity. We thus find that themore massive stars may suffer from substantial mass-loss even at lowmetallicity. We also predict that the Humphreys-Davidson limit should becomebrighter at decreasing metallicity. We supplement the evolutionary tracks withnew tables of theoretical bolometric corrections, useful to compare tracks andisochrones with the observations. For this purpose, we homogenize existingstellar atmosphere libraries of hot and cool stars (PoWR, ATLAS9 and Phoenix)and we add, where needed, new atmosphere models computed with WM-basic. Themass, age and metallicity grids are fully adequate to perform detailedinvestigations of the properties of very young stellar systems, both in localand distant galaxies. The new tracks supersede the previous old Padova modelsof massive stars.

PARSEC evolutionary tracks of massive stars up to $350 M_\odot$ at metallicities 0.0001$\leq Z \leq$0.04