  Globular cluster (GC) systems demonstrate tight scaling relations with the
properties of their host galaxies. In previous work, we developed an analytic
model for GC formation in a cosmological context and showed that it matches
nearly all of the observed scaling relations across 4 orders of magnitude in
host galaxy mass. Motivated by the success of this model, we investigate in
detail the physical origins and evolution of these scaling relations. The ratio
of the combined mass in GCs $M_{\rm GC}$ to the host dark matter halo mass
$M_h$ is nearly constant at all redshifts, but its normalization evolves by a
factor of $\sim$10 from birth to $z=0$. The relation is steeper than linear at
halo masses $M_h \lesssim 10^{11.5} M_{\odot}$, primarily due to non-linearity
in the stellar mass-halo mass relation. The near constancy of the ratio $M_{\rm
GC}/M_h$, combined with the shape of the stellar mass-halo mass relation, sets
the characteristic $U-$shape of the GC specific frequency as a function of host
galaxy mass. The contribution of accreted satellite galaxies to the buildup of
GC systems is a strong function of the host galaxy mass, ranging from
$\approx$0% at $M_h \approx 10^{11} M_{\odot}$ to 80% at $M_h \approx 10^{15}
M_{\odot}$. The metal-poor clusters are significantly more likely to form
ex-situ relative to the metal-rich clusters, but a substantial fraction of
metal-poor clusters still form in-situ in lower mass galaxies. Similarly, the
fraction of red clusters increases from $\approx 10$% at $M_h = 10^{11}
M_{\odot}$ to $\approx 60$% at $M_h \approx 10^{13} M_{\odot}$, and flattens at
higher $M_h$. Clusters formation occurs essentially continuously at high
redshift, while at low redshift galactic mergers become increasingly important
for cluster formation.
