  We study a mean-field model for a clustering process that may be described
informally as follows. At each step a random integer $k$ is chosen with
probability $p_k$, and the smallest cluster merges with $k$ randomly chosen
clusters. We prove that the model determines a continuous dynamical system on
the space of probability measures supported in $(0,\infty)$, and we establish
necessary and sufficient conditions for approach to self-similar form. We also
characterize eternal solutions for this model via a Levy-Khintchine formula.
The analysis is based on an explicit solution formula discovered by Gallay and
Mielke, extended using a careful choice of time scale.
