Limit theorems for decomposable branching processes with final types

Limit theorems are proved for a branching process homogeneous in continuous time, which has $n$ types of particles. The types $T_1,\dots,T_n$ are contained in classes of ranks $0,1,\dots,n-1$ respectively. Each type is either subcritical, critical, or final, and the set of final types is nonempty.
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