  We simulate the phase-space distribution of stellar mass in 9 massive
Lambda-CDM galaxy clusters by applying the semi-analytic particle tagging
method of Cooper et al. to the Phoenix suite of high-resolution N-body
simulations (M200 = 7.5 to 33 x 10^14 Msol). The resulting surface brightness
(SB) profiles of brightest cluster galaxies (BCGs) match well to observations.
On average, stars formed in galaxies accreted by the BCG account for ~90 per
cent of its total mass (the remainder is formed in situ). In circular
BCG-centred apertures, the superposition of multiple debris clouds (each ~10
per cent of the total BCG mass) from different progenitors can result in an
extensive outer diffuse component, qualitatively similar to a 'cD envelope'.
These clouds typically originate from tidal stripping at z < 1 and comprise
both streams and the extended envelopes of other massive galaxies in the
cluster. Stars at very low SB contribute a significant fraction of the total
cluster stellar mass budget: in the central 1 Mpc^2 of a z ~ 0.15 cluster
imaged at SDSS-like resolution, our fiducial model predicts 80-95 per cent of
stellar mass below a SB of mu_V = 26.5 mag arcsec^2 is associated with accreted
stars in the envelope of the BCG. The ratio of BCG stellar mass (including this
diffuse component) to total cluster stellar mass is ~30 per cent.
