Artificial Intelligence Uniform-cost search

Hi guys,

I have some questions about the search functions in artificial intelligence that I cannot understand. I know that Uniform-cost search is a special case of the A* search algorithm if its heuristic is a constant function.
Also I know that Breadth-first search (BFS) is a special case of A* when all edge costs are positive and identical.
Best-first search is also a special case of A* search.
But ho can I show that? How can I prove that all the above are correct?

is it

g=0 for best-first search
h=0 for uniform-cost search
and g=depth for breadth-first search??