  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 $L_{\rm Ly\alpha} \sim 3.0 \times 10^{42} - 2.1 \times 10^{43}$
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.
