For n points placed uniformly at random on the unit square, suppose $M_n$ (respectively, $M'_n$) denotes the longest edge-length of the nearest neighbor graph (respectively, the minimal spanning tree) on these points. It is known that the distribution of $n \pi M_n^2 - \log n$ converges weakly to the double exponential; we give a new proof of this. We show that $P[M'_n = M_n] \to 1$, so that the same weak convergence holds for $M'_n$ .
Mathew D. Penrose. "The longest edge of the random minimal spanning tree." Ann. Appl. Probab. 7 (2) 340 - 361, May 1997. https://doi.org/10.1214/aoap/1034625335