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We use the Illustris simulation to study the relative contributions of insitu star formation and stellar accretion to the build-up of galaxies over anunprecedentedly wide range of masses ($M_{\ast} = 10^9-10^{12} \, {\rmM_{\odot}}$), galaxy types, environments, and assembly histories. We find thatthe `two-phase' picture of galaxy formation predicted by some models is a goodapproximation only for the most massive galaxies in our simulation -- namely,the stellar mass growth of galaxies below a few times $10^{11} \, {\rmM_{\odot}}$ is dominated by in situ star formation at all redshifts. Thefraction of the total stellar mass of galaxies at $z=0$ contributed by accretedstars shows a strong dependence on galaxy stellar mass, ranging from about 10per cent for Milky Way-sized galaxies to over 80 per cent for $M_{\ast} \approx10^{12} \, {\rm M_{\odot}}$ objects, yet with a large galaxy-to-galaxyvariation. At a fixed stellar mass, elliptical galaxies and those formed at thecentres of younger haloes exhibit larger fractions of ex situ stars thandisc-like galaxies and those formed in older haloes. On average, $\sim$50 percent of the ex situ stellar mass comes from major mergers (stellar mass ratio$\mu > 1/4$), $\sim$20 per cent from minor mergers ($1/10 < \mu < 1/4$),$\sim$20 per cent from very minor mergers ($\mu < 1/10$), and $\sim$10 per centfrom stars that were stripped from surviving galaxies (e.g. flybys or ongoingmergers). These components are spatially segregated, with in situ starsdominating the innermost regions of galaxies, and ex situ stars being depositedat larger galactocentric distances in order of decreasing merger mass ratio.

The stellar mass assembly of galaxies in the Illustris simulation: growth by mergers and the spatial distribution of accreted stars