tokens: range of 60–80 kpc. Similar numbers have been found by Zhang et al. ( 2019 ) from the analysis of about 300 galaxy clusters at redshift 0.2 z 0.3. These authors described the BCG+ICL radial profile by using a triple Sérsic model and found a dominant core in the innermost 10 kpc, a bulge between 30 and 100 kpc and the ICL that dominates the distribution beyond 200 kpc, but already outside 100 kpc the profile transitions from the BCG to the ICL. They suggested that this transition is a potential cut between the two components, in good agreement with Pillepich et al. ( 2018 ) who noticed that simulated halos more massive than 5 × 10 14 M ⊙ have more ICL mass outside 100 kpc than within. All the values of the transition radius, i.e., the radius at which the ICL starts to become the dominant component, reported above are comparable with the range predicted by our model. We stress again that a wide range of possible values of R transition is preferable to a narrow one for the reasons discussed above. It strongly depends on the morphology of the BCG, on the amount of ICL with respect to the other components, and on the dynamical state of clusters, which reflects the merging history of the BCG+ICL system and thus its evolution with time. 5. Conclusions Following the analysis done in our recent paper (Contini Gu 2020 ), we have further improved our model by assuming that the radial mass distribution of a BCG+ICL system can be described by the sum of three profiles: a Jaffe profile for the bulge, an exponential disk, and a modified NFW for the ICL. We have taken advantage of a wide sample of simulated galaxy groups and clusters from our state-of-the-art semianalytic model to study the innermost ∼100 kpc of BCG+ICL systems. Unlike the model used in our previous study, the new one offers the opportunity to go below 100 kpc since bulge and disk are treated separately. The main goals of this study were to confirm that our model can reproduce several observed relations between the stellar mass at a given radius and the total BCG+ICL/halo mass, at different redshift and, give an idea of where the transition between the BCG and the ICL happens, i.e., when the ICL component starts to dominate the total distribution. In light of the analysis done and the overall discussion, we conclude the following: 1. The radial mass distribution of a BCG+ICL system can be described by the sum of three profiles: a Jaffe profile for the bulge, an exponential disk, and an NFW-like profile for the ICL. The model can reproduce several observed scaling relations between the BCG+ICL stellar mass within a given aperture and the BCG+ICL/halo mass, at different redshift with an overall precision below 0.05 dex at z = 0 and 0.3 dex at z ≳ 0.5 along the wide stellar mass/halo mass ranges probed. 2. In good agreement with recent observational studies, our model predicts that R transition , i.e., the radius at which the radial distribution of BCG+ICL systems transitions from the BCG to the
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