  We perform calculations of pre-main sequence evolution of stars from 1 to $85
M_{\odot}$ with growing accretion rates $\dot{M}$. The values of $\dot{M}$ are
taken equal to a constant fraction $\tilde{f}$ of the rates of the mass
outflows observed by Churchwell (\cite{church}) and Henning
(\cite{henning2000}). The evolution of the various stellar parameters is given,
as well as the evolution of the disc luminosity; electronic tables are provided
as a supplement to the articles. Typically, the duration of the accretion phase
of massive stars is $\simeq 3 \cdot 10^5$yr. and there is less than 10%
difference in the time necessary to form a 8 or $80 M_{\odot}$ star. If in a
young cluster all the proto-stellar cores start to accrete at the same time, we
then have a relation $M(t)$ between the masses of the new stars and the time
$t$ of their appearance. Since we also know the distribution of stellar masses
at the end of star formation (IMF), we can derive the star formation history
$N(t)$. Interestingly enough, the current IMF implies two peaks of star
formation: low mass stars form first and high mass star form later.
