  We use a hybrid observational/theoretical approach to study the relation
between galaxy kinematics and the derived stellar and halo masses of galaxies
up to z=3 as a function of stellar mass, redshift and morphology. Our
observational sample consists of a concatenation of 1125 galaxies with
kinematic measurements at 0.4<z<3 from long-slit and integral-field studies. We
investigate several ways to measure halo masses from observations based on
results from semi-analytical models, showing that galaxy halo masses can be
retrieved with a scatter of ~0.4 dex by using only stellar masses. We discover
a third parameter, relating to the time of the formation of the halo, which
reduces the scatter in the relation between the stellar and halo masses, such
that systems forming earlier have a higher stellar mass to halo mass ratio,
which we also find observationally. We find that this scatter correlates with
morphology, such that early-type, or older stellar systems, have higher
M_*/M_halo ratios. We furthermore show using this approach, and through weak
lensing and abundance matching, that the ratio of stellar to halo mass does not
significantly evolve with redshift at 1<z<3. This is evidence for the regulated
hierarchical assembly of galaxies such that the ratio of stellar to dark matter
mass remains approximately constant since $z = 2$. We use these results to show
that the dark matter accretion rate evolves from $dM_{\rm halo}/d{\rm t} \sim
4000$ M_solar year$^{-1}$ at $z \sim 2.5$, to a few 100 M_solar year$^{-1}$ by
$z \sim 0.5$.

Astrophysics of Galaxies