  We use the block model to generate merger trees for the first star clusters
in a LCDM cosmology. Using a simple collapse model and cooling criterion, we
determine which halos are able to form stars before being disrupted by mergers.
We contrast the mass functions of all the resulting star clusters and those of
primordial composition, i.e. star clusters that have not been contaminated by
subclusters inside them. In confirmation of previous work, two generations of
primordial star clusters are identified: low-temperature clusters that cool via
molecular hydrogen, and high-temperature clusters that cool via electronic
transitions. The former dominate by number, but the two populations contain a
similar mass with the precise balance depending upon the details of the model.
We speculate on the current-day distribution of Population III stars.
