  We have investigated the formation of globular cluster (GC) systems in the
fiducial semi-analytic galaxy formation model of Cole et al. We assume that GCs
are formed at high-redshift (z > 5) in proto-galactic fragments, and during the
subsequent gas-rich merging of these fragments. We find that the mean ages of
the metal-rich GCs are dependent upon host galaxy luminosity and halo circular
velocity, whereas the mean ages of the metal-poor GCs are not. We find that
gaseous merging of the proto-galactic fragments leads to a significant
age-spread amongst the metal-rich GCs, which increases for lower-luminosity
galaxies. We find the total GC populations scale with host galaxy luminosity as
L^1.25, due to the systematic increase in the mass-to-light ratios (with mass)
of the galaxy haloes in the model. A comparison between the luminosity growth
of the model ellipticals and their GC formation indicates that mergers do not
significantly effect S_N at z < 2. We conclude that gaseous merging, the bulk
of which occurs at 1 < z < 4 in the Lambda-CDM model, leads to the formation of
the metal-rich peak of the GC systems of elliptical galaxies. We suggest that
the formation and subsequent truncation of the metal-poor GCs is closely
related to the star formation rate in the proto-galactic fragments, which may
have been significantly higher at early times (abridged).
