16 Ewald Puchwein, Volker Springel, Debora Sijacki, & Klaus Dolag confirm a lower value than found in our simulations. This would represent a non-trivial challenge for future simulation models, as our work has shown that the simulated ICL frac- tion is remarkably robust, not only with respect to integra- tion parameters and numerical resolution, but also to quite drastic changes in the modelling of star formation. This also means that it is not obvious at all how a cluster simulation could be obtained that reproduces the galaxy population as well as in our best runs but at the same time yields a much lower ICL component. One interesting effect we found in our simulations is that a sizable fraction of our intracluster stars actually forms ‘in situ’, in gas clouds that were stripped out of the dark matter halos of infalling galaxies but that are not bound to a dark matter satellite any more. It is not entirely clear whether this mode of ‘intracluster star formation’ is signifi- cantly affected by numerical inaccuracies in the simulations. For example, fluid instabilities might be able to disrupt these clouds and suppress the star formation in them if they are better resolved than possible with SPH. If this were indeed the case, this could explain some part of the discrepancy. On the other hand, a high ICL fraction would actually help to relax the current tensions between constraints on the cos- mic baryon fraction and the baryon fractions measured in galaxy clusters. clusters and groups, it was necessary to find a robust way to assign star particles in the simulations either to one of the cluster’s satellite galaxies, to the BCG, or to the ICL. Espe- cially the distinction between the latter two components is not without ambiguities. We therefore developed and tested several different methods for distinguishing between the dif- ferent components. This helps to assess the robustness of the measurements and allows the validation of measurement techniques that are close to the methods usually employed in observational studies. Our investigation of the properties of the satellite galaxy populations, the BCGs and the ICL components in our simulations yielded the following main results: • We find a very significant fraction of ∼ 40% (without AGN) or ∼ 45% (with AGN) of intracluster stars within r crit 200 in our simulated clusters and groups. These values are robust with respect to numerical resolution and integration accuracy, and are almost independent of halo mass. They are, however, larger than those typically inferred from ob- servations. • For all the different methods we tested for making a distinction between BCG and ICL, we find that the vast majority of stars in the main halo of our simulated clusters are part of the ICL, rather than the BCG. As a result of this dominance, our ICL fractions also do not strongly depend on the exact method used for making the distinction. • The intracluster stars form on average earlier than the stars residing in cluster satellite galaxies. Stars ending up in the BCG at z = 0, however, typically form at even earlier times, especially when AGN are included in the simulations, which prevent excessive star formation in BCGs at low red- shift. • The fraction of stars that is stripped from infalling galaxies increases with galaxy stellar mass, which can be understood as a consequence of their larger ratio of size to tidal radius. The orbit of an infalling galaxy also plays an important role. Galaxies that closely approach the cluster centre typically loose the largest fraction of stars. • We find that most intracluster stars are stripped from galaxies that fell into the cluster early, roughly before z ∼ 1. Most likely, galaxies falling in later just do not have enough time to sink towards the cluster centre by dynamical friction and to get tidally disrupted there. • The stars stripped from individual galaxies are not smoothly distributed within the cluster even after several orbits of their former host galaxy, instead they form streams and other tidal features. The ICL is therefore not smooth but a superposition of many such tidal features. • In our simulations, a significant fraction of intracluster stars (up to ∼ 30%) do not form in galaxies but in cold gas clouds stripped from infalling substructures. These clouds remain intact after being stripped and give rise to ‘intra- cluster star formation’. • When including AGN, the total stellar masses in our simulated galaxy groups are in good agreement with obser- vations. However, the simulations do not reproduce the steep observed decline of the stellar mass fraction with halo mass, so that our massive simulated clusters contain more stars than suggested by observations. It will be very interesting to see whether improved ob- servational determinations of the ICL fraction in clusters ACKNOWLEDGMENTS We would like to thank Simon White for very constructive discussions. D.S. acknowledges Postdoctoral Fellowship from the UK Science and Technology Funding Council (STFC). K.D. acknowledges support by the DFG Priority Programme 117. Part of the simulations have been performed on the Cambridge High Performance Computing Cluster Darwin. 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