In humans, the placenta is usually a single disc. The umbilical vessels usually travel on the surface from the umbilical cord insertion out to, and return from, the cotyledons. The cotyledons are the functional units of the placenta, and each interacts with the blood vessels of the uterus. As the umbilical vessels reach the center of a cotyledon, they dive into the center and arborize until they form the fetal vessels that are close to the maternal vessels and exchange metabolites and oxygen. I do not know genetic or other signals that control the formation of the cotyledons. Sounds like an interesting research topic!