We study the origin of the diffuse stellar component (DSC) in 117 galaxy
clusters extracted from a cosmological hydrodynamical simulation. We identify
all galaxies present in the simulated clusters at 17 output redshifts, and then
build the family trees for all the z=0 cluster galaxies. Then for each diffuse
star particle identified at z=0, we look for the galaxy to which it once
belonged at an earlier redshift, thus linking the presence of the diffuse
stellar component to the galaxy formation history. The main results of our
analysis are: (i) On average, half of the DSC star particles comes from galaxies
associated with the family tree of the most massive galaxy (BCG), one quarter
comes from the family trees of other massive galaxies, and the remaining quarter
from dissolved galaxies. I.e., the formation of the DSC is parallel to the
build-up of the BCG and other massive galaxies. (ii) Most DSC star particles
become unbound during mergers in the formation history of the BGCs and of other
massive galaxies, independent of cluster mass. Our results suggest that the
tidal stripping mechanism is responsible only for a minor fraction of the DSC.
(iii) At cluster radii larger than 250 kpc/h, the DSC fraction from the BCG is
reduced and the largest contribution comes from the other massive galaxies; in
the cluster outskirts, galaxies of all masses contribute to the DSC. (iv) The
DSC does not have a preferred redshift of formation: however, most DSC stars are
unbound at z<1. (v) The amount of DSC stars at z=0 does not corre late strongly
with the global dynamical history of clusters, and increases weakly with cluster mass.