  Using a sample of 98 galaxy clusters recently imaged in the near infra-red
with the ESO NTT, WIYN and WHT telescopes, supplemented with 33 clusters from
the ESO archive, we measure how the stellar mass of the most massive galaxies
in the universe, namely Brightest Cluster Galaxies (BCG), increases with time.
Most of the BCGs in this new sample lie in the redshift range $0.2<z<0.6$,
which has been noted in recent works to mark an epoch over which the growth in
the stellar mass of BCGs stalls. From this sample of 132 clusters, we create a
subsample of 102 systems that includes only those clusters that have estimates
of the cluster mass. We combine the BCGs in this subsample with BCGs from the
literature, and find that the growth in stellar mass of BCGs from 10 billion
years ago to the present epoch is broadly consistent with recent semi-analytic
and semi-empirical models. As in other recent studies, tentative evidence
indicates that the stellar mass growth rate of BCGs may be slowing in the past
3.5 billion years. Further work in collecting larger samples, and in better
comparing observations with theory using mock images is required if a more
detailed comparison between the models and the data is to be made.
