We investigate the citation distributions of the 500 universities in the 2013 edition of the Leiden Ranking produced by The Centre for Science and Technological Studies. We use a Web of Science data set consisting of 3.6 million articles published in 2003 to 2008 and classified into 5,119 clusters. The main findings are the following. First, the universality claim, according to which all university‐citation distributions, appropriately normalized, follow a single functional form, is not supported by the data. Second, the 500 university citation distributions are all highly skewed and very similar. Broadly speaking, university citation distributions appear to behave as if they differ by a relatively constant scale factor over a large, intermediate part of their support. Third, citation‐impact differences between universities account for 3.85% of overall citation inequality. This percentage is greatly reduced when university citation distributions are normalized using their mean normalized citation scores (MNCSs) as normalization factors. Finally, regarding practical consequences, we only need a single explanatory model for the type of high skewness characterizing all university citation distributions, and the similarity of university citation distributions goes a long way in explaining the similarity of the university rankings obtained with the MNCS and the Top 10% indicator.