  This paper considers the asymptotic distribution of the longest edge of the
minimal spanning tree and nearest neighbor graph on X_1,...,X_{N_n} where
X_1,X_2,... are i.i.d. in \Re^2 with distribution F and N_n is independent of
the X_i and satisfies N_n/n\to_p1. A new approach based on spatial blocking and
a locally orthogonal coordinate system is developed to treat cases for which F
has unbounded support. The general results are applied to a number of special
cases, including elliptically contoured distributions, distributions with
independent Weibull-like margins and distributions with parallel level curves.
