  MHD models and the observation of accretion streamers confirmed that
protostars can undergo late accretion events after the initial collapse phase.
To provide better constraints, we study the evolution of stellar masses in MHD
simulations of a (4 pc)^3 molecular cloud. Tracer particles allow us to
accurately follow the trajectory of accreting material for all protostars and
thereby constrain the accretion reservoir of the stars. The diversity of the
accretion process implies that stars in the solar mass regime can have vastly
different accretion histories. Some stars accrete most of their mass during the
initial collapse phase, while others gain >50 % of their final mass from late
infall. The angular momentum budget of stars that experience substantial
infall, so-called late accretors, is significantly higher than for stars
without or with only little late accretion. As the probability of late infall
increases with increasing final stellar mass, the specific angular momentum
budget of higher mass stars is on average higher. The hypothetical centrifugal
radius computed from the accreting particles at the time of formation is orders
of magnitude higher than observed disk sizes, which emphasizes the importance
of angular momentum transport during disk formation. Nevertheless, we find a
correlation that the centrifugal radius is highest for stars with substantial
infall, which suggests that very large disks are the result of recent infall
events. There are also indications for a subtle trend of increasing centrifugal
radius with increasing final stellar mass, which is in agreement with an
observed marginal correlation of disk size and stellar mass. Finally, we show
that late accretors become embedded again during infall. As a consequence, late
accretors are (apparently) rejuvenated and would be classified as Class 0
objects according to their bolometric temperature despite being 1 Myr old.
