In several markets, firms compete not for consumer expenditure but instead for consumer attention. We model and characterize how households allocate their scarce attention in arguably the largest market for attention: the Internet. Our characterization of household attention allocation operates along three dimensions: how much attention is allocated, where that attention is allocated, and how that attention is allocated. Using click-stream data for thousands of U.S. households, we assess if and how attention allocation on each dimension changed between 2008 and 2013, a time of large increases in online offerings. We identify vast and expected changes in where households allocate their attention (away from chat and news towards video and social media), and yet we simultaneously identify remarkable stability in how much attention is allocated and how it is allocated. Specifically, we identify (i) persistence in the elasticity of attention according to income and (ii) complete stability in the dispersion of attention across sites and in the intensity of attention within sites. We illustrate how this finding is difficult to reconcile with standard models of optimal attention allocation and suggest alternatives that may be more suitable. We conclude that increasingly valuable offerings change where households go online, but not their general online attention patterns. This conclusion has important implications for competition and welfare in other markets for attention.