  We investigated the possibility of producing helium enhanced stars in
globular clusters by accreting polluted matter during the pre-main sequence
phase. We followed the evolution of two different classes of pre-main sequence
accreting models, one which neglects and the other that takes into account the
protostellar evolution.
  We analysed the dependence of the final central helium abundance, of the
tracks position in the HR diagram and of the surface lithium abundance
evolution on the age at which the accretion of polluted material begins and on
the main physical parameters that govern the protostellar evolution. The later
is the beginning of the late accretion and the lower are both the central
helium and the surface lithium abundances at the end of the accretion phase and
in ZAMS (Zero Age Main Sequence). In order to produce a relevant increase of
the central helium content the accretion of polluted matter should start at
ages lower than 1 Myr. The inclusion of the protostellar evolution has a strong
impact on the ZAMS models too. The adoption of a very low seed mass (i.e. 0.001
M$_{\odot}$) results in models with the lowest central helium and surface
lithium abundances. The higher is the accretion rate and the lower is the final
helium content in the core and the residual surface lithium. In the worst case
-- i.e. seed mass 0.001 M$_\odot$ and accretion rate $\ge 10^{-5}$ M$_\odot$
yr$^{-1}$ -- the central helium is not increased at all and the surface lithium
is fully depleted in the first few million years.
