I am facing a hard time understanding Blocking Flow problem. This is what I have understood till now : We have a graph and in blocking flow problem we find all shortest paths from source to destination and saturate atleast one edge in all of the shortest paths respectively  and we delete that path. In examples I am reading online, it is explained with an example of graph with all edges of unit length . Our professor explained the solution to this using dynamic trees. I am unable to apply the concept of dynamic trees (splay) for the solution of this problem. What will be stored in the nodes of the tree and on what basis will we perform the spaly operation?
 There can only be one shortest path, or many shortest paths of same length. What is the concept of all shortest paths?
 If a graph has all edges of unit lengths, then all the edges will be deleted (because all will appear in some path from source to sink). Then, source and destination will be disconnected in the end. What would be the use of doing this?
What is the goal for solving this problem? Can someone point in right direction in layman's terms? Also I have read some articles regarding this but unable to understand them and also none of them uses splay trees to solve this problem.