  We define a Markov process on the partitions of $[n]=\{1,\ldots,n\}$ by
drawing a sample in $[n]$ at each time of a Poisson process, by merging blocks
that contain one of these points and by leaving all other blocks unchanged.
This coalescent process appears in the study of the connected components of
random graph processes in which connected subgraphs are added over time with
probabilities that depend only on their size.
  First, we determine the asymptotic distribution of the coalescent time. Then,
we define a Bienayme-Galton-Watson (BGW) process such that its total population
size dominates the block size of an element. We compute a bound for the
distance between the total population size distribution and the block size
distribution at a time proportional to $n$. As a first application of this
result, we establish the coagulation equations associated with this coalescent
process. As a second application, we estimate the size of the largest block in
the subcritical and supercritical regimes as well as in the critical window.
