Limit theorems for critical Markov branching processes with several types of particles and infinite second moments

In this paper a necessary and sufficient condition is obtained for the existence of a proper limit distribution, not concentrated at one point, of the number of particles in a critical Markov branching process with several types of particles on the set of nondegenerate trajectories under the classical normalization. In the case where the limit distribution in question exists, limit distributions for the distance to the nearest common ancestor are obtained.
Bibliography: 10 titles.