Flow expansions are a fundamental mechanism of sediment deposition. Here we define flow expansions as selfformed alluvial expanding deposits developing over a larger experimental delta that 1) are characterized by unchannelized flow, comprising a single sheet flow that covers the entire surface of the expansion, and (2) do not interact laterally with still fluid and thus are not related to jets. The flow-spreading mechanism is transverse topographic curvature rather than mixing with ambient fluid; hence we term these expansions ''topographic expansions'' to distinguish them from jet-related flow expansions. In topographic expansions, transverse bed convexity drives lateral flow, allowing topographic expansions to maintain much higher, and more variable, opening angles than those of jet-related expansions. The characteristic depositional body produced by the expansions is a relatively thin, tabular sand body with a flat base and slightly convex top, comparable to some ''sheet flood'' deposits in the stratigraphic record. Most of the deposition takes place as the topographic expansion develops, followed by a longer interval of stable sediment bypass, where all measured flow expansions show similar geometries. This stable-bypass phase is typically terminated by the flow abandoning the deposit or by channelization of the deposit itself, after which the cycle can begin again. One of the research questions raised by this study is the mechanism by which topographic expansions are able to maintain themselves in an unchannelized condition at flow aspect ratios that should be unstable according to current theories of bar and channel instability.