  Random tilings or packings in the plane are characterized by a size
distribution of individual elements (domains) and by the statistics of neighbor
relations between the domains. Most systems occurring in nature or technology
have a unimodal distribution of both areas and number of neighbors.
Empirically, strong correlations between these distributions have been observed
and formulated as universal laws. Using only the local, correlation-free
granocentric model approach with no free parameters, we construct accurate
analytical descriptions for disc crystallization, size-topology correlations,
and Lema\^itre's law.
