Where does the crude oil go after it has been through the pipes from the offshore oil rig?

It can go via pipeline to an onshore facility for refining or storage, it can go to and FPSO (A floating production, storage and offloading vessel anchored in the vicinity of the oil rigs) where it could be pumped into oil tanker ships, or to a man made island where it is stored and pumped into oil tanker ships.

The oil eventually ends up in refineries where fuels, lubricants, plastics, chemical, rubber, and other bi-products are then manufactured.