The intracluster light (ICL) is a diffuse stellar component that permeates galaxy clusters and provides important information about their assembly history. However, separating the ICL from the extended stellar component of the brightest cluster galaxy (BCG) remains a challenging and somewhat ambiguous task, both observationally and theoretically.

In this talk, I will present a new approach to separating the BCG and ICL components in galaxy formation models, focusing on the physical transition between them rather than adopting a fixed spatial aperture. I will discuss how the resulting BCG and ICL masses depend on halo mass and redshift, and how different definitions of the two components can affect their inferred properties. Finally, I will discuss the implications of this separation for comparisons between theoretical predictions and observations and for our understanding of the build-up of the diffuse stellar component in galaxy clusters.