  There are numerous randomized algorithms to generate spanning trees in a
given ambient graph; several target the uniform distribution on trees (UST),
while in practice the fastest and most frequently used draw random weights on
the edges and then employ a greedy algorithm to choose the minimum-weight
spanning tree (MST). Though MST is a workhorse in applications, the
mathematical properties of random MST are far less explored than those of UST.
In this paper we develop tools for the quantitative study of random MST. We
consider the standard case that the weights are drawn i.i.d. from a single
distribution on the real numbers, as well as successive generalizations that
lead to \emph{product measures}, where the weights are independently drawn from
arbitrary distributions.
