  The stellar-to-halo mass relation (SHMR) is not only one of the main sources
of information we have on the connection between galaxies and their dark matter
haloes, but also an important indicator of the performance of galaxy formation
models. Here we use one of the largest sample of galaxies with both
high-quality rotation curves and near-infrared surface photometry, and perform
a detailed comparative analysis of the SHMR. Our analysis shows that there are
significant statistical differences between popular forms of the SHMR, and
illustrates the predictive power of a new physically motivated scaling
relation, which connects the stellar mass fraction ($M_{\star}/M_{\mathrm{h}}$)
to the stellar specific angular momentum ($j_{\star}$) and the stellar radial
velocity dispersion ($\sigma_{\star}$) via disc gravitational instability.
Making use of such a relation, we demonstrate (i) how challenging it is to
reproduce the efficiency of galaxy formation even for state-of-the-art
cosmological hydrodynamical simulations, and (ii) that the evolution of the
stellar mass fraction is regulated by disc gravitational instability: when
$M_{\star}/M_{\mathrm{h}}$ varies, $j_{\star}$ and $\sigma_{\star}$ also vary
as predicted by our scaling relation, thus erasing the memory of such
evolution. This implies that the process of disc gravitational instability is
intriguingly uniform across disc galaxies of all morphological types: from
lenticulars to blue compact dwarfs. In particular, the cosmic variance of
Toomre's $Q$ is 0.2 dex, a universal value for both stars and atomic gas.
