  A PopIII/Pop II transition from massive to normal stars is predicted to occur
when the metallicity of the star forming gas crosses the critical range Z_cr =
10^(-5 +/- 1) Z_sun. To investigate the cosmic implications of such process we
use numerical simulations which follow the evolution, metal enrichment and
energy deposition of both Pop III and Pop II stars. We find that: (i) due to
inefficient heavy element transport by outflows and slow "genetic" transmission
during hierarchical growth, large fluctuations around the average metallicity
arise; as a result Pop III star formation continues down to z=2.5, but at a low
peak rate of 10^-5 M_sun yr^-1 Mpc^-3 occurring at z~6 (about 10^-4 of the
PopII one); (ii) Pop III star formation proceeds in a "inside-out" mode in
which formation sites are progressively confined at the periphery of collapsed
structures, where the low gas density and correspondingly long free-fall
timescales result in a very inefficient astration. These conclusions strongly
encourage deep searches for pristine star formation sites at moderate (2<z<5)
redshifts where metal free stars are likely to be hidden.
