A long-standing hypothesis in biogeography is that a species' abundance is highest at the centre of its geographical or environmental space and decreases toward the edges. Several studies tested this hypothesis and provided mixed results and overall weak support to the theory. Most studies, however, are affected by several limitations related to the sample size, the comparability among abundance measures, the definition of species geographic range and corresponding environmental space, and the proxy variables used to represent centrality/marginality gradients. Here we test the abundant-centre hypothesis on 108 bird and mammal species and embrace the plural nature of the hypothesis by considering 9 geographic and ecological centrality/marginality measures. We analyse the species-specific effect sizes using a meta-analytical approach, and test whether the support for the hypothesis is mediated by species dispersal abilities, and the geographic and environmental coverage of the data. The summary effect sizes estimated for the 9 measures are largely inconsistent with the theoretical expectations and show a significant amount of residual heterogeneity. Variables such as dispersal distance, geographic and environmental coverage of the data, appear important in explaining the variation observed between different species, but the results are contrary to those originally hypothesized, and inconsistent across centrality/marginality measures and the datasets used. We show that addressing common pitfalls in previous studies does not provide more support to the abundant-centre hypothesis, with support being very dependent on the centrality/marginality measure tested, the geographic extent considered for the test, and geographic and environmental coverage of the data. The abundant-centre hypothesis so far remains an appealing speculation with little and variable empirical support.