  Due to the popularity of randomly evolving graph processes, there exists a
randomized version of many recursively defined graph models. This is also the
case with the cherry tree, which was introduced by Buksz\'ar and Pr\'ekopa to
improve Bonferroni type upper bounds on the probability of the union of random
events. Here we consider a substantially extended random analogue of that
model, embedding it into a general time dependent branching process.
