During cell division, centromeres split apart during anaphase, which is one of the stages of mitosis and meiosis. In mitosis, after the chromosomes line up at the metaphase plate during metaphase, the sister chromatids are pulled apart as the spindle fibers shorten and the centromeres divide.
In meiosis, centromeres split apart during anaphase II, following a similar process. The separation of centromeres allows the sister chromatids to move to opposite poles of the cell, ensuring that each daughter cell will receive an identical set of chromosomes. This is a crucial step that ensures genetic consistency and the proper distribution of genetic material, vital for the formation of new cells.