(Abriged) At present, there are two scenarios for the formation of massive stars: 1) The accretion scenario and 2) The coalescence scenario, which implies the merging of intermediate mass stars. We examine here some properties of the first one. We calculate three different sets of birthlines, i.e. tracks followed by a continuously accreting star. First, three models with a constant accretion rate ($dot{M}_{rm{accr}}$ = $10^{-6}$, $10^{-5}$, $10^{-4}$ M$_{odot}$ yr$^{-1}$). Then several birthlines following the accretion models of Bernasconi and Maeder (cite{BM96}), which have $dot{M}_{rm{accr}}$ increasing only slightly with mass. Finally we calculate several birthlines for which $dot{M}_{accr} = dot{M}_{mathrm{ref}} ({frac{M}{M_{odot}}}) ^{phi}$, with values of $phi$ equal to 0.5, 1.0 and 1.5 and also for different values of $dot{M}_{mathrm{ref}}$. The best fit to the observations of PMS stars in the HR diagram is achieved for $phi$ between 1.0 or 1.5 and for $dot{M}_{mathrm{ref}} simeq 10^{-5}$ M$_{odot}$ yr$^{-1}$. Considerations on the lifetimes favour values of $phi$ equal to 1.5. These accretion rates do well correspond to those derived from radio and IR observations of mass outflows. We emphasize the importance of the accretion scenario for shaping the IMF, and in particular for determining the upper mass limit of stars. In the accretion scenario, this upper mass limit will be given by the mass for which the accretion rate is such that the accretion induced shock luminosity is of the order of the Eddington luminosity.
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