  We present a numerical investigation of the gravitational collapse of
horizon-size density fluctuations to primordial black holes (PBHs) during the
radiation-dominated phase of the Early Universe. The collapse dynamics of three
different families of initial perturbation shapes, imposed at the time of
horizon crossing, is computed. The perturbation threshold for black hole
formation, needed for estimations of the cosmological PBH mass function, is
found to be $\delta_{\rm c} \approx 0.7$ rather than the generally employed
$\delta_{\rm c} \approx 1/3$, if $\delta$ is defined as $\Delta M/\mh$, the
relative excess mass within the initial horizon volume. In order to study the
accretion onto the newly formed black holes, we use a numerical scheme that
allows us to follow the evolution for long times after formation of the event
horizon. In general, small black holes (compared to the horizon mass at the
onset of the collapse) give rise to a fluid bounce that effectively shuts off
accretion onto the black hole, while large ones do not. In both cases, the
growth of the black hole mass owing to accretion is insignificant. Furthermore,
the scaling of black hole mass with distance from the formation threshold,
known to occur in near-critical gravitational collapse, is demonstrated to
apply to primordial black hole formation.
