Self-renewing stem cell divisions typically couple the polarised orientation of the mitotic spindle with an invariant age-dependent pattern of centrosome inheritance. Self- renewal supports tissue homeostasis by providing, in a balanced manner, one daughter cell retaining stemness and another daughter cell set to differentiate. Such balance is central to avoid tumourigenesis. Age-dependent spindle pole inheritance directing the polarised orientation of the mitotic spindle was first discovered in the budding yeast Saccharomyces cerevisiae, a unicellular organism that divides asymmetrically like stem cells. Furthermore, this budding yeast is at the forefront in cell cycle studies. Thus, S. cerevisiae represents a powerful model for linking the molecular basis for age-dependent asymmetric fate with cell cycle regulation. Our group previously showed that Spc72, a component of the spindle pole body (SPB, the yeast centrosome), is the key factor priming the invariant segregation of the old SPB (the SPB present prior to duplication) into the bud and the new SPB into the mother cell. In this thesis, I present quantitative imaging analysis paired to biochemical studies that reveal Spc72 asymmetry as an intrinsic feature of SPB duplication under cyclin-dependent kinase (CDK) control. In turn, I uncovered a mechanism for Spc72 spatial partition centred on two further SPB components that bind Spc72 in a cell-cycle dependent manner governed by CDK phosphorylation. The SPB components involved in my study as well as CDK, the master regulator of the eukaryotic cell cycle, are highly conserved. It follows that my work will provide crucial insight into cell cycle control of intrinsic centrosome asymmetries with impact on stem cell self-renewing divisions and beyond.