The aim of this paper is to test the predictions of Sutton's independent submarkets model with data on the Spanish retail banking market. The prediction of this model is that, within each submarket, when the products are close substitutes and price competition is weak, the only form of equilibrium outcome will be an extreme `fragmented' structure. However, the aggregates of submarkets will simultaneously show a concentrated structure. To test these predictions, firstly I propose methods to identify independent submarkets. Then I analyse the degree of inequality in bank sizes for markets with different levels of aggregation (submarkets, regions and national market). Using concentration by towns' data, I find that in single market towns the degree of inequality of the size among banks, measured by their number of branches, is zero. Moreover, multimarket towns with a significant degree of concentration are shown to be formed by a different number of independent submarkets where each bank owns one branch. Nonetheless, when the regional and national bank markets are considered, the degree of inequality in bank sizes becomes high. These results are consistent with the predictions of the theoretical model.