  Motivated by an interpretation of $z \sim 3$ objects by Jimenez and Haiman
(2006), we examine processes that control the fraction of primordial ($Z = 0$)
gas, and so primordial stars, in high-SFR Lyman break galaxies. A primordial
fraction different from 1 or 0 requires microscopic diffusion catalyzed by a
velocity field with timescale comparable to the duration of star formation. The
only process we found that satisfies this requirement for LBGs without
fine-tuning is turbulence-enhanced mixing induced by exponential stretching and
compressing of metal-rich ejecta. The time-dependence of the primordial
fraction for this model is calculated. We show that conclusions for all the
models discussed here are virtually independent of the IMF, including extremely
top-heavy IMFs.
