This article presents an analysis of the population-density distributions present in 147 Polish towns and cities of 30,000 inhabitants or more, as of 2002. The determination of these distributions was by reference to concentric rings 1 km across, with numbers of inhabitants being determined on the basis of aggregate data for 14,000 statistical districts, the numbers per centre ranging from 16 in the case of Łuków to 1346 in Warsaw. The districts in question cover a total area of 9800 km 2 and account overall for some 16.8 million inhabitants of Poland. This makes this the most exhaustive analysis of population-density distributions ever carried out for the country. The results of the analyses point to the widespread presence of function-related distributions of population density in the largest Polish cities, albeit irrespective of their size as referred to more precisely. A clear majority (88%) of centres are characterised by a distribution model in line with either the exponential or power functions, or derivatives. The 'crater effect' indicative of depopulation in city centres is met with only rarely, in just a very few towns and cities, this perhaps reflecting the relative youthfulness of Poland's urban areas.

This paper presents a state-of-the-art review of the principal models of urban population density, including the seven members of the quadratic gamma family and Amson's equilibrium models. A historical introduction is followed by a review of basic assumptions, and then each model is analysed individually, with separate discussions of principal theoretical findings and experimental results.