MTA-SZTE Analysis and Stochastics Research Group Bolyai Institute University of Szeged Szeged H-6720 Hungary;
Department of Statistics and Probability Instituto de Investigaciones en Matemáticas Aplicadas y en Sistemas Universidad Nacional Autònoma de México Ciudad de México 04510 México;
Bolyai Institute University of Szeged Szeged H-6720 Hungary;
multi-type continuous state and continuous time branching processes with immigration; almost sure; L1-and L2-growth behaviour;