  We use the observed sizes and star formation rates of Lyman-break galaxies
(LBGs) to understand their properties expected in the hierarchical scenario of
galaxy formation. The observed size distribution constrains the masses of the
host haloes of LBGs from below, while the observed star-formation distribution
constrains the masses from above. Assuming a flat CDM model with a cosmological
constant ($\Omega_\Lambda=0.7$), we find that consistency with observations
requires the circular velocities of LBG host haloes to be in the range
100--$300 {\rm km s^{-1}}$. The predicted comoving correlation length of these
objects is $\sim 3 h^{-1}{\rm Mpc}$, and the predicted velocity dispersion of
their stellar contents is typically $70 {\rm km s^{-1}}$. The same prescription
applied to larger haloes in the CDM cosmogony predicts the existence of
galaxies with star formation rates $\sim 1000 {\rm M_\odot yr^{-1}}$ at
redshift $z\sim 3$. We explore the possibility of identifying these galaxies to
be the bright sub-millimeter (sub-mm) sources detected by SCUBA. The model
predicts that the host haloes of these sub-mm sources are massive. These
galaxies are predicted to be strongly correlated, with a comoving correlation
length of $\sim 7 h^{-1}{\rm Mpc}$. The descendants of the bright sub-mm
sources should reside in clusters of galaxies at the present time, and it is
likely that these objects are the progenitors of giant ellipticals. The model
predicts the existence of a relatively bright and red population of galaxies at
$z\sim 3$, which may be observed in the K-band.
