The existence of stellar halos around galaxies is a natural prediction of the hierarchical nature of the LambdaCDM model. Recent observations of Milky Way-like galaxies have revealed a wide range in stellar halo mass, including cases with no statistically significant detection of a stellar halo, as in the case of M101, NGC3351 and NGC1042. We use the Illustris simulation to investigate the scatter in stellar halo content and, in particular, to study the formation of galaxies with the smallest fraction of this diffuse component. Stellar halos are far from spherical, which diminishes the surface brightness of the stellar halo for face-on disks. Once accounting for projection effects, we find that the stellar halo fraction f_SH correlates strongly with galaxy morphology and star formation rate, but not with environment, in agreement with observations. Galaxies with the lowest stellar halo fractions are disk-dominated, star-forming and assemble their dark matter halos on average earlier than galaxies with similar stellar masses. Accreted satellites are also lower in stellar mass and have earlier infall times than centrals with high f_SH. In situ rather than accreted stars dominate the stellar halos of galaxies with the lowest stellar halo fractions, with a transition radius from in situ to accretion-dominated r~45 kpc. Our results extrapolated to real galaxies such as M101 may indicate that these galaxies inhabit old halos which endured mergers only at higher redshifts and evolved relatively unperturbed in the last ~10 Gyrs.

13 pages, 12 figures