Let n points be placed independently in ν-dimensional space according to the standard ν-dimensional normal distribution. Let M
n
be the longest edge-length of the minimal spanning tree on these points; equivalently let M
n
be the infimum of those r such that the union of balls of radius r/2 centred at the points is connected. We show that the distribution of (2 log n)1/2
M
n
- b
n
converges weakly to the Gumbel (double exponential) distribution, where b
n
are explicit constants with b
n
~ (ν - 1)log log n. We also show the same result holds if M
n
is the longest edge-length for the nearest neighbour graph on the points.
