The kinetoplast (k) DNA network of trypanosomatids is made up of approximately 50 maxicircles and in the order of 104 minicircles. It has been proposed, based on various observations and experiments, that the minicircles are randomly segregated between daughter cells when the parent cell divides. In this paper, this random segregation hypothesis is theoretically tested in a population dynamics model to see if it can account for the observed phenomena. The hypothesis is shown to successfully explain, in Leishmania tarentolae, the observation that there are a few major and many minor minicircles, the fluctuations of minicircle class copy numbers over time, the loss of non–essential minicircle classes, the long survival times of a few of these classes and that these classes are likely to be the major classes within the population. Implications of the model are examined for trypanosomids in general, leading to several predictions. The model predicts variation in network size within a population, variation in the average network size and large–scale changes in class copy number over long time–scales, an evolutionary pressure towards larger network sizes, the selective advantage of non–random over random segregation, very strong selection for the amplified class in Crithidia fasciculata if its minicircles undergo random segregation and that Trypanosoma brucei may use sexual reproduction to maintain its viability.