  We characterize the statistical law according to which Italian primary
school-size distributes. We find that the school-size can be approximated by a
log-normal distribution, with a fat lower tail that collects a large number of
very small schools. The upper tail of the school-size distribution decreases
exponentially and the growth rates are distributed with a Laplace PDF. These
distributions are similar to those observed for firms and are consistent with a
Bose-Einstein preferential attachment process. The body of the distribution
features a bimodal shape suggesting some source of heterogeneity in the school
organization that we uncover by an in-depth analysis of the relation between
schools-size and city-size. We propose a novel cluster methodology and a new
spatial interaction approach among schools which outline the variety of
policies implemented in Italy. Different regional policies are also discussed
shedding lights on the relation between policy and geographical features.
