  (Multi-type) branching processes are a natural and well-studied model for
generating random infinite trees. Branching processes feature both
nondeterministic and probabilistic branching, generalizing both transition
systems and Markov chains (but not generally Markov decision processes). We
study the complexity of model checking branching processes against linear-time
omega-regular specifications: is it the case almost surely that every branch of
a tree randomly generated by the branching process satisfies the omega-regular
specification? The main result is that for LTL specifications this problem is
in PSPACE, subsuming classical results for transition systems and Markov
chains, respectively. The underlying general model-checking algorithm is based
on the automata-theoretic approach, using unambiguous B\"uchi automata.
