Abstract: It is assumed that only one son-node is born in each delivery in the model of Markov birth-death branching tree. This paper assumed that the number of son-nodes born in each delivery is a random variable, and develop a model of birth-death branching tree with nodes being multiparous. Existence of this model is shown. We study the numbers of living nodes, dead nodes, connected components, son-nodes of any node at any age, and son-nodes at dying moment.

Key words: birth-death branching tree, branching process, Markov process, random graph