In an influential paper, Harte et al. highlighted the scaling or ‘self-similar’ character of the power law species–area relationship (SAR), and used this feature to derive a species abundance distribution (SAD) and an endemics–area relationship. Here I show that their analysis was incorrect and leads to unrealistic results. I develop a different approach and obtain different results, both for SAD and for endemism. In particular, I show that the power law SAR is naturally associated with the power law statistical distribution, which is the only self-similar distribution and closely matches empirical SADs. The results in this paper shed light on some of the main issues that have been discussed with regard to SARs: their relationship with the lognormal and with the neutral theory, the relative importance of sampling effects vs other mechanisms, and the deviations from a power law. The equations that I develop are simple and easy to apply to field studies.