  Starting with a monodisperse configuration with $n$ size-1 particles, an
additive Marcus-Lushnikov process evolves until it reaches its final state (a
unique particle with mass $n$). At each of the $n-1$ steps of its evolution, a
merging cost is incurred, that depends on the sizes of the two particles
involved, and on an independent random factor. This paper deals with the
asymptotic behaviour of the cumulated costs up to the $k$th clustering, under
various regimes for $(n,k)$, with applications to the study of Union--Find
algorithms.
