A Population III/Population II transition from massive to normal stars is predicted to occur when the metallicity of the star-forming gas crosses the critical range Zcr = 10-5+/-1Zsolar. To investigate the cosmic implications of such a process, we use numerical simulations which follow the evolution, metal enrichment and energy deposition of both Population II and Population III 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, Population III star formation continues down to z = 2.5, but at a low peak rate of 10-5Msolaryr-1Mpc-3 occurring at z ~ 6 (about 10-4 of the Population II one); and (ii) Population III star formation proceeds in an `inside-out' mode in which formation sites are progressively confined to the periphery of collapsed structures, where the low gas density and correspondingly long free-fall time-scales 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.
