Krapivsky, P. L. and S. Redner

We investigate the dynamics of an immortal branching process. In the classic, critical branching process, particles give birth to a single offspring or die at the same rates. Even though the average population is constant in time, the ultimate fate of the population is extinction. We augment this branching process with immortality by positing that either: (a) a single particle cannot die, or (b) there exists an immortal stem cell that gives birth to ordinary cells that can subsequently undergo critical branching. We also treat immortal two-type branching. We discuss the new dynamical aspects of these immortal branching processes.