  We present a galaxy formation model to understand the evolution of stellar
mass (M*) - UV luminosity relations, stellar mass functions and specific star
formation rate (sSFR) of Lyman Break Galaxies (LBGs) along with their UV
luminosity functions in the redshift range 3 < z < 8. Our models assume a
physically motivated form for star formation in galaxies and model parameters
are calibrated by fitting the observed UV luminosity functions (LFs) of LBGs.
We find the fraction of baryons that gets converted into stars remains nearly
constant for z < 4 but shows an increase for z < 4. However, the rate of
converting baryons into stars does not evolve significantly in the redshift
range 3 < z < 8. Our model further successfully explains the M* - UV luminosity
(M_AB) correlations of LBGs. While our model predictions of stellar mass
functions compare well with the inferred data from observations at the low mass
end, we need to invoke the Eddington bias to fit the high mass end. At any
given redshift, we find the sSFR to be constant over the stellar mass range 5
\times 10^8 -5 \times 10^9 M_\odot and the redshift evolution of sSFR is well
approximated by a form (1+z)^2.4 for 3 < z < 8 which is consistent with
observations. Thus we find that dark matter halo build up in the LCDM model is
sufficient to explain the evolution of UV LFs of LBGs along with their M* -
M_AB relations, the stellar mass functions and the sSFR for 3 < z < 8.
