Plays an important role in cell division and centrosome function by participating in centriole duplication (PubMed:17681131, PubMed:20531387). Inhibits microtubule nucleation from the centrosome. Involved in the regulation of slow processive growth of centriolar microtubules. Acts as a microtubule plus-end tracking protein that stabilizes centriolar microtubules and inhibits microtubule polymerization and extension from the distal ends of centrioles (PubMed:15047868, PubMed:27219064, PubMed:27306797). Required for centriole elongation and for STIL-mediated centriole amplification (PubMed:22020124). Required for the recruitment of CEP295 to the proximal end of new-born centrioles at the centriolar microtubule wall during early S phase in a PLK4-dependent manner (PubMed:27185865). May be involved in the control of centriolar-microtubule growth by acting as a regulator of tubulin release (PubMed:27306797). {ECO:0000269|PubMed:15047868, ECO:0000269|PubMed:17681131, ECO:0000269|PubMed:20531387, ECO:0000269|PubMed:22020124, ECO:0000269|PubMed:27185865, ECO:0000269|PubMed:27219064, ECO:0000305|PubMed:27306797}. This is the function of CPAP (centrosome assembly and centriole elongation protein, ENSG00000151849).