In this paper we develop a probabilistic voting model of inter-governmental transfers to explain the distribution and size of local public goods. The main findings of the paper are: First, the parties’ political competition for votes in a federal election induces the central government to provide transfers to the different regions of the country that lead to Pareto efficient local public goods with and without inter-regional spillovers. Second, in this paper we show that the central government has political incentives to produce differentiated and uniform local public goods. This outcome is different to most normative and positive analysis that consider that the heterogeneity of the households’ preferences across districts has a strict positive monotone effect on the distribution of local public goods. We show that this is not the case. In particular, differentiated local public goods arise if the voters’ preferences over local public spending are not too heterogeneous across districts and the inter-regional spillovers of local public goods are moderate. However, if the preferences of voters over local public goods are too heterogeneous across districts and the size and asymmetry of spillovers of local public goods is sufficiently high then the central government has political incentives to provide a uniform local public good. Finally, in this paper we provide a comparative analysis to study the influence of political competition, the extent of inter-regional spillovers of local public goods, the distribution of the population in the economy and the size and distribution of local public spending.