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We present results of self-consistent, high-resolution cosmological simulations of galaxy formation at z∼3. The simulations employ a recently developed recipe for star formation based on the local abundance of molecular hydrogen, which is tracked self-consistently during the course of the simulation. The phenomenological H2 formation model accounts for the effects of dissociating UV radiation of stars in each galaxy, as well as for self-shielding and shielding of H2 by dust. This allows us therefore to explore effects of lower metallicities and higher UV fluxes prevalent in high redshift galaxies on their star formation. We find that the Kennicutt-Schmidt (KS) relation exhibited by our simulated galaxies at z≈3 is substantially steeper and has a lower amplitude than the z = 0 relation at ∑H<100 M⊙/pc2. The predicted relation, however, is consistent with existing observational constraints for the z≈3 Damped Lyman α (DLA) and LBGs. [ABSTRACT FROM AUTHOR]