  We present numerical results for the tagged-particle dynamics by solving the
mode-coupling theory in confined geometry for colloidal liquids (cMCT). We show
that neither the microscopic dynamics nor the type of intermediate scattering
function qualitatively changes the asymptotic dynamics in vicinity of the glass
transition. In particular, we find similar characteristics of confinement in
the low-frequency susceptibility spectrum which we interpret as footprints of
parallel relaxation. We derive predictions for the localization length and the
scaling of the diffusion coefficient in the supercooled regime and discover a
pronounced non-monotonic dependence on the confinement length. For dilute
liquids in the hydrodynamic limit we calculate an analytical expression for the
intermediate scattering functions, which is in perfect agreement with
event-driven Brownian dynamics simulations. From this, we derive an expression
for persistent anti-correlations in the velocity autocorrelation function
(VACF) for confined motion. Using numerical results of the cMCT equations for
the VACF we also identify a cross-over between different scalings corresponding
to a transition from unconfined to confined behaviour.
