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The stellar-to-halo mass relation (SHMR) is not only one of the main sourcesof information we have on the connection between galaxies and their dark matterhaloes, but also an important indicator of the performance of galaxy formationmodels. Here we use one of the largest sample of galaxies with bothhigh-quality rotation curves and near-infrared surface photometry, and performa detailed comparative analysis of the SHMR. Our analysis shows that there aresignificant statistical differences between popular forms of the SHMR, andillustrates the predictive power of a new physically motivated scalingrelation, which connects the stellar mass fraction ($M_{\star}/M_{\mathrm{h}}$)to the stellar specific angular momentum ($j_{\star}$) and the stellar radialvelocity dispersion ($\sigma_{\star}$) via disc gravitational instability.Making use of such a relation, we demonstrate (i) how challenging it is toreproduce the efficiency of galaxy formation even for state-of-the-artcosmological hydrodynamical simulations, and (ii) that the evolution of thestellar mass fraction is regulated by disc gravitational instability: when$M_{\star}/M_{\mathrm{h}}$ varies, $j_{\star}$ and $\sigma_{\star}$ also varyas predicted by our scaling relation, thus erasing the memory of suchevolution. This implies that the process of disc gravitational instability isintriguingly uniform across disc galaxies of all morphological types: fromlenticulars to blue compact dwarfs. In particular, the cosmic variance ofToomre's $Q$ is 0.2 dex, a universal value for both stars and atomic gas.

From lenticulars to blue compact dwarfs: the stellar mass fraction is regulated by disc gravitational instability