property line and then he (the neighbor) had a swath of land that went from the edge of the easement to the center of the easement. The OP had the same thing on the opposite side/on his property. So when the neighbor put up a fence on the "edge" of the easement (not the center) he just walked away from taking care of it or using it. So the OP took over control of the entire easement swath, nut just up to the center of the easement swath but the whole thing.

Make sense now?