We here derive upper limits on the mass and luminosity of Population III (POPIII) dominated proto-galaxies based on the collapse of primordial gas under the effect of angular momentum loss via Ly$alpha$ radiation drag and the gas accretion onto a galactic centre. Our model predicts that POPIII-dominated galaxies at z ~ 7 are hosted by haloes with $M_{rm halo} sim 1.5 times 10^{8} - 1.1 times 10^{9} rm ~M_{odot}$, that they have Ly$alpha$ luminosities of $L_{rm Lyalpha} sim 3.0 times 10^{42} - 2.1 times 10^{43}$ erg/s, stellar mass of $M_{rm star} sim 0.8 times 10^{5} - 2.5 times 10^{6} rm ~M_{odot}$, and outflowing gas with velocities $V_{rm out} sim 40$ km/s due to Ly$alpha$ radiation pressure. We show that the POPIII galaxy candidate CR7 violates the derived limits on stellar mass and Ly$alpha$ luminosity and thus is unlikely to be a POPIII galaxy. POPIII-dominated galaxies at z ~ 7 have HeII line emission that is ~1- 3 orders of magnitude lower then that of Ly$alpha$, they have high Ly$alpha$ equivalent width of > 300 $AA$ and should be found close to bright star forming galaxies. The HeII 1640 $AA$ line is in comfortable reach of next generation telescopes, like the JWST or TMT.
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