It has been recently shown that a two-type branching process provides an excellent description of experimental data on cell dynamics in skin tissue. The model involves only a single type of progenitor cells, and does not require support from a self-renewed population of stem cells. I will show that this model admits an exact solution. \par Multiple-type branching processes also play a major role in dynamics of cancer. I will describe one such model, based on the two-type branching process, which also happens to be solvable. The chief conclusion is that simple models, much simpler than it was previously thought, describe cell maintenance, and these models are even tractable.