  Consider~\(n\) nodes distributed independently across~\(N\) cities contained
with the unit square~\(S\) according to a distribution~\(f.\) Each city is
modelled as an~\(r_n \times r_n\) square contained within~\(S\) and~\(MSTC_n\)
denotes the length of the minimum spanning tree containing all the~\(n\) nodes.
We use approximation methods to obtain variance estimates for~\(MSTC_n\) and
prove that if the cities are well-connected and densely populated in a certain
sense, then~\(MSTC_n\) appropriately centred and scaled converges to zero in
probability.
  Using the proof techniques, we alternately derive corresponding results for
the length~\(MST_n\) of the minimum spanning tree for the usual case when the
nodes are independently distributed throughout the unit square~\(S.\) In
particular, we obtain that the variance of~\(MST_n\) grows at most as a power
of the logarithm of~\(n\) and use a subsequence argument to get almost sure
convergence of~\(MST_n\) appropriately centred and scaled.
