  We use a simple model of disc-galaxy formation in the LCDM cosmology to
simultaneously reproduce the slopes, zero-points, scatter and uncorrelated
residuals in the observed velocity-luminosity (VL) and radius-luminosity (RL)
relations. Observed I-band luminosities are converted to stellar masses using
the IMF-dependent relation between stellar mass-to-light ratio, M/L, and color.
The model treats halo concentration, spin parameter, and disc mass fraction as
independent log-normal random variables. Our main conclusion is that the VL and
RL zero-points and the uncorrelated residuals can only be reproduced
simultaneously if adiabatic contraction is avoided. One or the other could be
fixed by appealing to unrealistic values for M/L, halo concentration c, and
spin parameter lambda, but not all together. The small VL scatter is naturally
determined by the predicted scatter in c and in M/L, quite independent of the
large scatter in lambda. However, the RL scatter, driven by the scatter in
lambda, can be as low as observed only if sigma_lambda simeq 0.25, about half
the value predicted for CDM haloes. This may indicate that discs form in a
special subset of haloes. The VL slope is reproduced once star formation occurs
only above a threshold surface density, and the RL slope implies that the disc
mass fraction is increasing with halo mass, consistent with feedback effects. A
model that incorporates the above ingredients provides a simultaneous fit to
all the observed features. In particular, the elimination of adiabatic
contraction allows 80% disc contribution to the observed rotation velocity of
bright discs at 2.2 disc scale lengths. The lack of halo contraction may
indicate that disc formation is not as smooth as typically envisioned, but
instead may involve clumpy, cold streams.
