Just how surjective is a cryptographic hash like SHA-1?
In this regard SHA-1 despite it's weaknesses can be viewed as a pseudo random function.
This means we are are throwing $n$ balls into $n$ bins.
An output bin remains empty if all the balls miss it.
Which happens with probability $(1-1/n)^n$ which is $1/e$ and that is the portion of output bins which are empty.
We also can estimate that the most populated bin has approximately $log(n)$ balls.