This question might look strange, so I will try to be clear.
Consider a hashing function $f : M \mapsto H$ which takes a message with arbitrary length $m \in M$ as input and returns a hash $h \in H$ of fixed length.
What I want to know is this. Consider to have $N$ different input messages and their hashes, well what I do is providing to $f$ a very very big number of messages, and I want to see how many times each possible hash will be returned (one hash can be returned twice of course or even more because of collision).
When i consider such operation I will get a probability distribution which describes that hashing function. What I want to know is:
- What is the official name of this distribution?
- Can I know such distributions for the most popular hashing functions?
And of course the most important thing: is it nonsense what I talked about so far, or it is something that does not even exist?