  In the two-phase scenario of galaxy formation, a galaxy's stellar mass growth
is first dominated by in-situ star formation, and subsequently by accretion. We
analyse the radial distribution of the accreted stellar mass in ~500 galaxies
from the hydrodynamical cosmological simulation Magneticum. Generally, we find
good agreement with other simulations in that higher mass galaxies have larger
accreted fractions, but we predict higher accretion fractions for low-mass
galaxies. Based on the radial distribution of the accreted and in-situ
components, we define 6 galaxy classes, from completely accretion dominated to
completely in-situ dominated, and measure the transition radii between in-situ
and accretion-dominated regions for galaxies that have such a transition. About
70% of our galaxies have one transition radius. However, we also find about 10%
of the galaxies to be accretion dominated everywhere, and about 13% to have two
transition radii, with the centre and the outskirts both being accretion
dominated. We show that these classes are strongly correlated with the galaxy
merger histories, especially with the mergers' cold gas fractions. We find high
total in-situ (low accretion) fractions to be associated with smaller, lower
mass galaxies, lower central dark matter fractions, and larger transition
radii. Finally, we show that the dips in observed surface brightness profiles
seen in many early-type galaxies do not correspond to the transition from
in-situ to accretion-dominated regions, and any inferred mass fractions are not
indicative of the true accreted mass. Instead, these dips contain information
about the galaxies' dry minor merger assembly history.
