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As demonstrated in Paper I, the quenching properties of central and satellitegalaxies are quite similar as long as both stellar mass and halo mass arecontrolled. Here we extend the analysis to the size and bulge-to-total lightratio (B/T) of galaxies. In general central galaxies have size-stellar mass andB/T-stellar mass relations different from satellites. However, the differencesare eliminated when halo mass is controlled. We also study the dependence ofsize and B/T on halo-centric distance and find a transitional stellar mass(M$_{*,t}$) at given halo mass (M$_h$), which is about one fifth of the mass ofthe central galaxies in halos of mass M$_h$. The transitional stellar massesfor size, B/T and quenched fraction are similar over the whole halo mass range,suggesting a connection between the quenching of star formation and thestructural evolution of galaxies. Our analysis further suggests that theclassification based on the transitional stellar mass is more fundamental thanthe central-satellite dichotomy, and provide a more reliable way to understandthe environmental effects on galaxy properties. We compare the observationalresults with the hydro-dynamical simulation, EAGLE and the semi-analytic model,L-GALAXIES. The EAGLE simulation successfully reproduces the similarities ofsize for centrals and satellites and even M$_{*,t}$, while L-GALAXIES fails torecover the observational results.

The Dearth of Difference between Central and Satellite Galaxies III. Environmental Dependence of Mass-Size and Mass-Structure Relations