  While there has been an extended discussion concerning city population
distribution, little has been said about administrative units. Even though
there might be a correspondence between cities and administrative divisions,
they are conceptually different entities and the correspondence breaks as
artificial divisions form and evolve. In this work we investigate the
population distribution of second level administrative units for 150 countries
and propose the Discrete Generalized Beta Distribution (DGBD) rank-size
function to describe the data. After testing the goodness of fit of this two
parameter function against power law, which is the most common model for city
population, DGBD is a good statistical model for 73% of our data sets and
better than power law in almost every case. Particularly, DGBD is better than
power law for fitting country population data. The fitted parameters of this
function allow us to construct a phenomenological characterization of countries
according to the way in which people are distributed inside them. We present a
computational model to simulate the formation of administrative divisions and
give numerical evidence that DGBD arises from it. This model along with the
DGBD function prove adequate to reproduce and describe local unit evolution and
its effect on population distribution.
