  Sizes of galaxies are an important diagnostic for galaxy formation models. In
this study I use the abundance matching ansatz, which has proven to be
successful in reproducing galaxy clustering and other statistics, to derive
estimates of the virial radius, R200, for galaxies of different morphological
types and wide range of stellar mass. I show that over eight of orders of
magnitude in stellar mass galaxies of all morphological types follow an
approximately linear relation between 3D half-mass radius of their stellar
distribution, rhalf and virial radius, rhalf~0.015R200 with a scatter of ~0.2
dex. Such scaling is in remarkable agreement with expectation of models which
assume that galaxy sizes are controlled by halo angular momentum, which implies
rhalf\propto lambda R200, where lambda is the spin of galaxy parent halo. The
scatter about the relation is comparable with the scatter expected from the
distribution of $\lambda$ and normalization of the relation agrees with that
predicted by the model of Mo, Mao & White (1998), if galaxy sizes were set on
average at z~1-2. Moreover, I show that when stellar and gas surface density
profiles of galaxies of different morphological types are rescaled using radius
r_n= 0.015 R200, the rescaled surface density profiles follow approximately
universal exponential (for late types) and de Vaucouleurs (for early types)
profiles with scatter of only 30-50% at R~1-3r_n. Remarkably, both late and
early type galaxies have similar mean stellar surface density profiles at
R>r_n. The main difference between their stellar distributions is thus at
R<r_n. The results of this study imply that galaxy sizes and radial
distribution of baryons are shaped primarily by properties of their parent halo
and that sizes of both late type disks and early type spheroids are controlled
by halo angular momentum.
