Centrioles are crucial cellular organelles that form cores of centrosomes and cilia. Centrioles must replicate once every cell cycle producing exactly one daughter centriole. Both failure to replicate and production of supernumerary centrioles jeopardizes cellular life and can cause disease, such as microcephaly and cancer. Temporary regulation of centriole replication, which is provided by the cell cycle, has been largely elucidated. However, the numeric control that ensures that only one procentriole is produced by each pre-existing centriole remains an unsolved puzzle. In this talk I will present our theoretical model of the centriole initiation process. We postulate that a small module comprising a kinase PLK4 and its activator-substrate STIL/Ana2/SAS-5 is the core of the protein network responsible for the initiation of a procentriole. Our model recapitulates symmetry-breaking transition in the spatial localization of PLK4 from a symmetric ring surrounding mother centriole to a single spot marking the position of nascent procentriole. Importantly, our model predicts that induction of a single procentriole is not just an advantageous happenstance but the result of winner-takes-all competition between multiple centriolar loci for the PLK4-STIL complexes. Weakening of competition by overexpression of PLK4 and STIL causes progressive addition of supernumerary procentrioles, as has been observed experimentally.