The conditional stellar mass function (CSMF, also called the conditional mass function or CMF) is a parameterized, unnormalized probability density function giving the average number of a dark matter halo's galaxies with stellar masses within a range interval, as a function of halo mass. In other words, the count of galaxies with stellar masses within some range (m +/- dm)/2 that reside within a halo within some mass range (M +/- DM)/2, i.e., a function of m and M. Sometimes such a CSMF is split into one specific to halos' central galaxies versus another specific to halos' satellite galaxies. Such CSMFs might result from compiling data, and devising heuristic mathematical formulae to match it. Alternately such a function might be devised based on physical arguments. This approach to characterizing galaxies within halos by mass is modeled after the conditional luminosity function.
Such CSMFs are used in halo models, models that explains the galaxies in dark matter halos, relating them to dark matter distributions produced by cosmology simulations, presumably to match observation of large surveys such as Sloan Digital Sky Survey.
Note that in the term CSMF, the phrase mass function is meant to indicate it deals with physical masses. The phrase also occurs in probability terminology (probability mass function) for a totally different, incompatible concept: a function yielding the probability of some discrete random variable taking on a given value.