  The time process of transport on randomly evolving trees is investigated. By
introducing the notions of living and dead nodes a model of random tree
evolution is constructed which describes the spreading in time of objects
corresponding to nodes. By using the method of the age-dependent branching
processes we derive the joint distribution function of the number of living and
dead nodes, and determine the correlation between these node numbers as a
function of time. Also analyzed are the stochastic properties of the end-nodes;
and the correlation between the numbers of living and dead end-nodes is shown
to change its character suddenly at the very beginning of the evolution
process. The survival probability of random trees is investigated and
expressions are derived for this probability.
