Splitting of centromere occurs during:

During anaphase of mitosis centromeres split and chromatids separate. During anaphase I of meiosis the homologous chromosomes separate, while sister chromatids remain associated at their centromeres. Anaphase II of meiosis begins with the simultaneous splitting of the centromere of each chromosome (which was holding the sister chromatids together), allowing them to move toward opposite poles of the cell.