We study last-layer outlier dimensions, i.e. dimensions that display extreme activations for the majority of inputs. We show that outlier dimensions arise in many different modern language models, and trace their function back to the heuristic of constantly predicting frequent words. We further show how a model can block this heuristic when it is not contextually appropriate, by assigning a counterbalancing weight mass to the remaining dimensions, and we investigate which model parameters boost outlier dimensions and when they arise during training. We conclude that outlier dimensions are a specialized mechanism discovered by many distinct models to implement a useful token prediction heuristic.