A border between two image regions is normally owned by only one of the regions; determining which one is essential for surface perception and figure-ground segmentation. Border ownership (BOWN) is signalled by some V2 neurons, even though its value depends on information coming from well outside their classical receptive fields (Zhou, Friedman, von der Heydt, J. Neurosci. 20(17):6594–411, 2000). Tuning to BOWN is significantly weaker or even absent in V1, so the tuning in V2 cannot be relayed from V1. Thus the key question arises whether the context-dependent neural tuning to BOWN in V2 is generated by mechanisms within this area, by top-down feedback from higher visual areas, or by a combination of both top-down and local mechanisms. I use a model of V2 to show that this visual area can plausibly generate the ownership signal by itself, without requiring top-down mechanisms 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 only receive information (from V1) about the location and orientation of borders. Tuning to BOWN arises in the model through finite-range, intra-cortical interactions. The model can account for the physiological observations in Zhou et al 2000 and Qiu and von der Heydt, VSS abstract 115, 2003, including the effect of occlusion, transparency and figures of different sizes, shapes and neighborhood relationships. The model also makes testable predictions, the matches to which can be used to constrain the model parameters further. The model can be extended to include the effects of additional image cues, such as surface luminance and depth, or top down attention, whose influence on BOWN have been observed psychophysically.