I found the easiest way to think of it is as a tree. The smaller, higher 'branches' starting in the mountains/hills/etc. then merging into larger 'branches' and eventually into the 'trunk' before reaching the sea/ocean.

Rivers rarely split, if they do it's only for a short time or in deltas (Ex: Nile or Mississippi) - there maybe some other wyas for it to happen but I'm not a geologist