We present a technique to visualize the streamline-based mapping between the boundary of a simply-connected subregion of arbitrary 3D vector fields. While the streamlines are seeded on one part of the boundary, the remaining part serves as escape border. Hence, the seeding part of the boundary represents a map of streamline behavior, indicating if streamlines reach the escape border or not. Since the resulting maps typically exhibit a very fine and complex structure and are thus not amenable to direct sampling, our approach instead aims at topologically consistent extraction of their boundary. We show that isocline surfaces of the projected vector field provide a robust basis for stream-surface-based extraction of these boundaries. The utility of our technique is demonstrated in the context of transport processes using vector field data from different domains.