Title: A family of random trees with random edge lengths
Author: David Aldous and Jim Pitman
Date: June 1998 
Pub: Random Structures and Algorithms Vol 15, 176-195 (1999)
Abstract:
We introduce a family of probability distributions on the space
of trees with I labeled vertices and possibly extra unlabeled
vertices of degree 3, whose edges have positive real lengths.
Formulas for distributions of quantities such as degree sequence,
shape, and total length are derived.
An interpretation is given in terms of sampling from the inhomogeneous
continuum random tree of Aldous and Pitman (1998).
Key words and phrases: continuum tree, enumeration, random tree, spanning tree,
weighted tree, Cayley's multinomial expansion.