  Hierarchical assembly within clusters of galaxies is tied directly to the
evolution of the Brightest Cluster Galaxies (BCGs), which dominate the stellar
light in the centres of rich clusters. In this paper we investigate the number
of mergers onto BCGs in 14 X-ray selected clusters over the redshift range 0.8
< z < 1.4 using HST imaging data. We find significant differences in the
numbers of companion galaxies to BCGs between the clusters in our sample
indicating that BCGs in similar mass clusters can have very different merging
histories. Within a 50 kpc radius around the BCGs we find an average of 6.45
\pm 1.15 companion galaxies with mass ratios (companion:BCG) between 1:1 and
1:20. The infalling companions show a 50/50 split between major (1:1 - 1:2) and
minor (1:3 - 1:20) mergers. When compared to similar work using lower redshift
clusters, these results demonstrate that both major and minor merging was more
common in the past. Since the dynamical timescales for merging onto the BCG are
relatively short compared with the look-back time to z ~ 1 our results suggest
that the BCG stellar mass may increase by as much as 1.8 times since z = 1.
However the growth rate of BCGs will be substantially less if stripped material
from nearby companions ends up in the diffuse intracluster light.
