  The decomposable branching processes are relatively less studied objects,
particularly in the continuous time framework. In this paper, we consider
various variants of decomposable continuous time branching processes. As usual
practice in the theory of decomposable branching processes, we group various
types into irreducible classes. These irreducible classes evolve according to
the well-studied nondecomposable/ irreducible branching processes. And we
investigate the time evolution of the population of various classes when the
process is initiated by the other class particle(s). We obtained class-wise
extinction probability and the time evolution of the population in the
different classes. We then studied another peculiar type of decomposable
branching process where any parent at the transition epoch either produces a
random number of offspring, or its type gets changed (which may or may not be
regarded as new offspring produced depending on the application). Such
processes arise in modeling the content propagation of competing contents in
online social networks. Here also, we obtain various performance measures.
Additionally, we conjecture that the time evolution of the expected number of
shares (different from the total progeny in irreducible branching processes) is
given by the sum of two exponential curves corresponding to the two different
classes.
