  We make a detailed investigation of the properties of Lyman-break galaxies
(LBGs) in the LambdaCDM model. We present predictions for two published
variants of the GALFORM semi-analytical model: the Baugh et al. (2005) model,
which has star formation at high redshifts dominated by merger-driven
starbursts with a top-heavy IMF, and the Bower et al. (2006) model, which has
AGN feedback and a standard Solar neighbourhood IMF throughout. We show
predictions for the evolution of the rest-frame far-UV luminosity function in
the redshift range z=3-20, and compare with the observed luminosity functions
of LBGs at z=3-10. We find that the Baugh et al. model is in excellent
agreement with these observations, while the Bower et al. model predicts too
many high-luminosity LBGs. Dust extinction, which is predicted
self-consistently based on galaxy gas contents, metallicities and sizes, is
found to have a large effect on LBG luminosities. We compare predictions for
the size evolution of LBGs at different luminosities with observational data
for 2<z<7, and find the Baugh et al. model to be in good agreement. We present
predictions for stellar, halo and gas masses, star formation rates, circular
velocities, bulge-to-disk ratios, gas and stellar metallicities and clustering
bias, as functions of far-UV luminosity and redshift. We find broad consistency
with current observational constraints. We then present predictions for the
abundance and angular sizes of LBGs out to very high redshift (z<20), finding
that planned deep surveys with JWST should detect objects out to z<15. The
typical UV luminosities of galaxies are predicted to be very low at high
redshifts, which has implications for detecting the galaxies responsible for
reionizing the IGM; for example, at z=10, 50% of the ionizing photons are
expected to be produced by galaxies fainter than M_AB(1500A)-5logh ~ -15.
