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tokens: novel prediction for the scatter in the mass in the stellar halos. Upcoming surveys (e.g., van Dokkum et al. 2014 ) of stellar halos will help to constrain this picture. The scatter of the SMHM relation contains valuable information on the galaxy formation process. It deserves careful consideration in both observations and simulations in the future. At the high-mass end (), the scatter is a generic consequence of the hierarchical assembly. Different simulations should be able to produce consistent scatter of the SMHM relation in this mass range. At lower halo mass () the scatter gradually becomes dominated by baryonic processes involved in the in situ buildup, and has potentially more constraining power on the underlying theory. Two different processes, in situ and ex situ growth, are needed to produce the apparent flat scatter in the SMHM relation. However, the similar magnitude of the observed scatter at the low and high-mass end is likely a coincidence. Other works (e.g., Boylan-Kolchin et al. 2012 ; Garrison-Kimmel et al. 2014 ; Dutton et al. 2015 ; Sawala et al. 2015 ) have shown that at the regime of dwarf galaxies, the scatter of the SMHM relation may be much larger than that in more massive systems. More stringent observational constraints on the mass dependence of the scatter would be valuable. We end this section by highlighting several caveats and areas for future improvement. The Bolshoi simulation has a limited resolution (one particle mass ), so halos with mass smaller than may not be properly described in the Bolshoi simulation. As shown in Figure 1 , a fraction of satellite galaxies are possibly affected by this limited resolution. The result for host halos at the low-mass end () should be treated with caution. However, as discussed earlier, since the stellar component in such halos should be very small, based on the SMHM relation, this should only have a small effect on our result. Moreover, we adopt a simple assumption that when a subhalo disrupts, all of its stellar content is accreted to the host halo, while in reality, the accretion of stellar mass could be delayed (Wetzel White 2010 ). We also do not distinguish between the stellar mass in the central galaxy and that in the ICL. Since most observations only include the stellar mass measurement of the central part of the host halo, a direct comparison with observations should also be treated with caution. The scatter in the SMHM relations observed should be roughly the quadratic sum of the intrinsic scatter discussed above and the measurement error. Behroozi et al. ( 2010 ) carefully studied different uncertainties in the SMHM relation. The authors included statistical uncertainties in the stellar mass function, cosmological parameters, and the uncertainty within the methodology to construct the SMHM relation, and revealed a ∼0.07 dex (and ∼0.12 dex) observational uncertainty at z = 0 (and z = 1). As shown in Figure 8 , we compare this with the observed scatter at z = 0