  We consider branching processes consisting of particles (individuals) of two
types (type L and type S) in which only particles of type L have offspring,
proving estimates for the survival probability and the (tail of) the
distribution of the total number of particles. Such processes are in some sense
closer to single- than to multi-type branching processes. Nonetheless, the
second, barren, type complicates the analysis significantly. The results proved
here (about point and survival probabilities) are a key ingredient in the
analysis of bounded-size Achlioptas processes in a recent paper by the last two
authors.
