The statistical behaviour of turbulent scalar flux and modelling of its transport have been analysed for both major reactants and products in the context of Reynolds Averaged Navier Stokes simulations using a detailed chemistry Direct Numerical Simulation (DNS) database of freely-propagating H2 −air flames (with an equivalence ratio of 0.7) spanning the corrugated flamelets, thin reaction zones and broken reaction zones regimes of premixed turbulent combustion. The turbulent scalar flux in the cases representing the corrugated flamelets and thin reaction zones regimes of combustion exhibit predominantly counter-gradient transport, whilst a gradient transport has been observed for the broken reaction zones regime flame considered here. It has been found that the qualitative behaviour of the various terms of the turbulent scalar flux transport equation for the major species such as H2, O2 and H2O in the cases representing the corrugated flamelets and thin reaction zones regimes of combustion are mostly similar, whilst the behaviour is markedly different for the case representing the broken reaction zone regime. However, the terms for the scalar flux transport equation for H2 and O2 show same signs whereas the corresponding terms for H2O show signs opposite to those for H2 and O2. The performances of the well-established existing models for the unclosed terms of the turbulent scalar flux transport equation have been found to be similar for H2, O2 and H2O Some of the existing models for turbulent flux, pressure gradient, molecular diffusion and reaction contributions have been found to yield reasonable performance for the cases representing the corrugated flamelets and thin reaction zones regimes but the existing closures for these terms have been found to be mostly inadequate for the broken reaction zones regime flames.