it does happen, obviously, but only on a very limited scale. My hometown of Hamburg for example has a river that "splits up".

http://maps.google.de/maps?q=hamburg...mburg&t=m&z=12

Still, that should probably only happen small scale, not over vast distances, and only in flat areas etc. What should not happen is the river you have that splits up near the source and then flows into two entirely different seas (just north-east of the continent's center).