Rapid warming of the Arctic is causing permafrost thaw and leading to changes in the thermokarst lake distribution. While extensive work has quantified trends and changes in total thermokarst lake area, less attention has been paid to the distribution of lake sizes and location, its physical underpinning, and how this distribution may be influenced by warming. A difficulty in assessing the lake size distribution is interannual and seasonal variability in observed lake extent due to abundant shallow wetlands on deltas. We present a methodology for distinguishing between ephemeral, shallow wetlands and perennial, deeper lakes using Landsat-derived water occurrence maps. We analyze seven deltas along a gradient of temperatures and document that perennial lake sizes follow a lognormal distribution, while ephemeral wetland sizes follow a power law or heavy tailed distribution. We propose a mechanistic model of thermokarst lake growth which is consistent with the observed lognormal distribution, and argue that the power law distribution of ephemeral wetlands is consistent with an inundated rough landscape, as observed in temperate wetlands. Lake size is a control of biogeochemical and hydrologic cycling on deltas and thus heterogeneity in lake size plays an important role in computing carbon and methane estimates and in assessing how these might change in the future.