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In Paper-I we developed a two-phase model to connect dynamically hot galaxies(such as ellipticals and bulges) with the formation of self-gravitating,turbulent gas clouds (SGC) associated with the fast assembly of dark matterhalos. Here we explore the implications of the model for the size-stellar massrelation of dynamically hot galaxies. Star-forming sub-clouds produced by thefragmentation of the SGC inherit its spatial structure and dynamical hotness,which produces a tight and 'homologous' relation, $r_{\rm f}\approx\, 100r_{\rm bulge}$, between the size of a dynamically hot galaxy ($r_{\rm bulge}$)and that of its host halo assembled in the fast assembly regime ($r_{\rm f}$),independent of redshift and halo mass. This relation is preserved by the 'dry'expansion driven by dynamical heating when a galaxy becomes gas-poor due toinefficient cooling, and is frozen during the slow assembly regime when thebulge stops growing in mass and dynamical heating is no longer effective. Thesize-stellar mass relation is thus a simple combination of the galaxy-halohomology and the non-linear relation between stellar mass and halo mass. Usinga set of halo assembly histories we demonstrate that this model can reproduceall properties in the observed size-mass relation of dynamically hot galaxies,including the flattening of the relation in the low-mass end and the upturn inthe very massive end. The predicted evolution of this relation matchesobservational data currently available to redshift $z \approx 4$, and can betested in the future at higher $z$. Our results indicate that the sizes ofdynamically hot galaxies are produced by the dissipation and collapse of gas indark matter halos to establish self-gravitating systems of sub-clouds in whichstars form.

A two-phase model of galaxy formation: II. The size-mass relation of dynamically hot galaxies