Centrioles, together with the surrounding peri-centriolar material (PCM), constitute the centrosome, a major microtubule-organizing center of animal cells. Despite being critical in many cells for signaling, motility and division, centrioles can be eliminated in some systems, including in the vast majority of differentiating cells during embryogenesis in Caenorhabditis elegans. Whether the cells retaining centrioles in the resulting L1 larvae do so because they lack an activity that eliminates centrioles in the other cells is not known. Moreover, the extent to which centrioles and PCM remain present in later stages of worm development, when all cells but those of the germ line are terminally differentiated, is not known. Here, by fusing cells that lack centrioles with cells that retain them, we established that L1 larvae do not possess a diffusible elimination activity sufficient to remove centrioles. Moreover, analyzing PCM core proteins in L1 larval cells that retain centrioles, we found that some such proteins, but not all, are present as well. Furthermore, we uncovered that foci of centriolar proteins remain present in specific terminally differentiated cells of adult hermaphrodites and males, in particular in the somatic gonad. Correlating the time at which cells were born with the fate of their centrioles revealed that it is not cell age, but instead cell fate, that determines whether and when centrioles are eliminated. Overall, our work maps the localization of centriolar and PCM core proteins in the post-embryonic C. elegans lineage, thereby providing an essential blueprint for uncovering mechanisms modulating their presence and function.