Suppose we have a graph $G(E,V)$ with a source node $s$. Now for any $t\in V \setminus s$ I can find the maximum flow from $s$ to all possible $t$ by using the Ford Fulkerson algorithm $|V|-1$ times, once for each $t$. I feel like there must be a faster way to compute all $|V|-1$ max flows that makes use of dynamic programming techniques. Any ideas?
"J. Hao and J. B. Orlin. A faster algorithm for finding the minimum cut in a directed graph." provides an algorithm to compute the min cut for a fixed s on the source side with time-complexity $O(nm \log(n^2/m))$, by reducing the complexity of multiple s-t cuts for varying sinks to the complexity of a single call to the Push-Relabel max-flow algorithm.
This might be adaptable to a version where you can store all the intermediate min-cut values (=max-flow values) for all sinks along the way.