Many microfluidic systems-including chemical reaction, sample analysis, separation, chemotaxis, and drug development and injection-require control and precision of solute transport. Although concentration levels are easily specified at injection, pressure-driven transport through channels is known to spread the initial distribution, resulting in reduced concentrations downstream. Here we document an unexpected phenomenon: The channel's cross-sectional aspect ratio alone can control the shape of the concentration profile along the channel length. Thin channels (aspect ratio << 1) deliver solutes arriving with sharp fronts and tapering tails, whereas thick channels (aspect ratio similar to 1) produce the opposite effect. This occurs for rectangular and elliptical pipes, independent of initial distributions. Thus, it is possible to deliver solute with prescribed distributions, ranging from gradual buildup to sudden delivery, based only on the channel dimensions.