  We consider the continuous-time version of the random digital search tree,
and construct a coupling with a border aggregation model as studied in Thacker
and Volkov (2018), showing a relation between the height of the tree and the
time required for aggregation. This relation carries over to the corresponding
discrete-time models. As a consequence we find a very precise asymptotic result
for the time to aggregation, using recent results by Drmota et al.\ (2020) for
the digital search tree.
