  The mass--velocity--size relation of late-type galaxies decouples into
independent correlations between mass and velocity (the Tully-Fisher relation),
and between mass and size. This behaviour is different to early-type galaxies
which lie on a Fundamental Plane. We study the coupling of the Tully-Fisher and
mass-size relations in observations (the SPARC sample) and in empirical galaxy
formation models based on halo abundance matching, and rotation curve fits with
a hydrodynamically motivated halo profile. We systematically investigate the
correlation coefficient between the Tully-Fisher residuals $\Delta V_r$ and
mass-size residuals $\Delta R$ as a function of the radius $r$ at which the
velocity is measured, and thus present the $\Delta V_r-\Delta R$ relation
across rotation curves. We find no significant correlation in either the data
or models for any $r$, aside from $r \ll R_\text{eff}$ where baryonic mass
dominates. We show that this implies an anticorrelation between galaxy size and
halo concentration (or halo mass) at fixed baryonic mass, and provides evidence
against the hypothesis that galaxy and halo specific angular momentum are
proportional. Finally, we study the $\Delta V_r-\Delta R$ relations produced by
the baryons and dark matter separately by fitting halo profiles to the rotation
curves. The balance between these components illustrates the "disk-halo
conspiracy" required for no overall correlation.
