Using a cosmological $N$-body simulation, we investigate the origin and distribution of stars in the intracluster light (ICL) of a Fornax-like cluster. In a dark matter only simulation we identify a halo which, at $z=0$, has $M_200 simeq 4.1 times 10^{13}M_{sun}$ and $r_{200} = 700kpc$, and replace infalling subhalos with models that include spheroid and disc components. As they fall into the cluster, the stars in some of these galaxies are stripped from their hosts, and form the ICL. We consider the separate contributions to the ICL from stars which originate in the haloes and the discs of the galaxies. We find that disc ICL stars are more centrally concentrated than halo ICL stars. The majority of the disc ICL stars are associated with one initially disc-dominated galaxy that falls to the centre of the cluster and is heavily disrupted, producing part of the cD galaxy. At radial distances greater than 200kpc, well beyond the stellar envelope of the cD galaxy, stars formerly from the stellar haloes of galaxies dominate the ICL. Therefore at large distances, the ICL population is dominated by older stars.
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