A border between two image regions normally belongs to only one of the regions; determining which one it belongs to is essential for surface perception and figure-ground segmentation. Border ownership is signaled by a class of V2 neurons, even though its value depends on information coming from well outside their classical receptive fields. I use a model of V2 to show that this visual area is able to generate the ownership signal by itself, without requiring any top-down mechanism or external explicit labels for figures, T junctions, or corners. In the model, neurons have spatially local classical receptive fields, are tuned to orientation, and receive information (from V1) about the location and orientation of borders. Border ownership signals that model physiological observations arise through finite range, intraareal interactions. Additional effects from surface features and attention are discussed. The model licenses testable predictions.