  We compute the rate of supercollapsars by using cosmological, N-body, hydro,
chemistry simulations of structure formation, following detailed stellar
evolution according to proper yields (for He, C, N, O, Si, S, Fe, Mg, Ca, Ne,
etc.) and lifetimes for stars having different masses and metallicities, and
for different stellar populations (population III and population II-I). We find
that supercollapsars are usually associated to dense, collapsing gas with
little metal pollution and with abundances dominated by oxygen. The resulting
supercollapsar rate is about $10^{-2}\,\rm yr^{-1} sr^{-1}$ at redshift $z=0$,
and their contribution to the total rate is $ < 0.1 $ per cent, which explains
why they have never been detected so far. Expected rates at redshift $z\simeq
6$ are of the order of $\sim 10^{-3}\,\rm yr^{-1} sr^{-1}$ and decrease further
at higher $z$. Because of the strong metal enrichment by massive, short-lived
stars, only $\sim 1$ supercollapsar generation is possible in the same star
forming region. Given their sensitivity to the high-mass end of the primordial
stellar mass function, they are suitable candidates to probe pristine
population III star formation and stellar evolution at low metallicities.
