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We study the growth pathways of Brightest Central Galaxies (BCGs) andIntra-Cluster Light (ICL) by means of a semi-analytic model. We assume that theICL forms by stellar stripping of satellite galaxies and violent processesduring mergers, and implement two independent models: (1) one considers bothmergers and stellar stripping (named {\small STANDARD} model), and oneconsiders only mergers (named {\small MERGERS} model). We find that BCGs andICL form, grow and overall evolve at different times and with differenttimescales, but they show a clear co-evolution after redshift $z \sim 0.7-0.8$.Around 90\% of the ICL from stellar stripping is built-up in the innermost 150Kpc from the halo centre and the dominant contribution comes from disk-likegalaxies (B/T$<$0.4) through a large number of small/intermediate strippingevents ($M_{strip}/M_{sat}<0.3$). The fractions of stellar mass in BCGs and inICL over the total stellar mass within the virial radius of the halo evolvedifferently with time. At high redshift, the BCG accounts for the bulk of themass, but its contribution gradually decreases with time and stays constantafter $z\sim 0.4-0.5$. The ICL, instead, grows very fast and its contributionkeeps increasing down to the present time. The {\small STANDARD} and the{\small MERGERS} models make very similar predictions in most of the cases, butpredict different amounts of ICL associated to other galaxies within the virialradius of the group/cluster other than the BCG, at $z=0$. We then suggest thatthis quantity is a valid observable that can shed light on the relativeimportance of mergers and stellar stripping for the formation of the ICL.

The different growth pathways of Brightest Cluster Galaxies and the Intra-Cluster Light