We study the spontaneous curving observed when a strip of tracing paper is deposited on a water surface. The differential swelling across the ribbon thickness leads to a curling of the sheet, with the curvature increasing to a maximum and then relaxing as the sheet becomes completely wet. We develop a theoretical model, in good agreement with our experimental observations and relevant to the understanding of curling instabilities induced by asymmetric swelling of natural or synthetic shells. © 2011 The Royal Society of Chemistry.