# Why does Union-Find have time complexity O(N + M lg* N) with the “log star N”?

The time complexity of Weighted Union-Find with Path Compression, for M union-find ops and N objects is said to be

$$O(N + M \lg^*N)$$

and the $$lg^*N$$ is "log star N" and is iterated logarithm. It can be almost taken to be a constant, as $$lg^*2^{65536}$$ is only equal to 5. Why is it $$lg^*N$$ and what kind of operations / algorithm typical can produce $$lg^*N$$?