The research center produces and stores Resource Points (RP).
Resource Points are created by research centers within nations but are stored at the empire level. An empire may store RP equal to the maximum capacity of all research centers in all nations in the empire. RP is used as a resource to purchase technologies.
Even though the research buildings reside within your nations, the research points created by those buildings are stored at the empire level. The maximum amount of research points your empire may hold is based on the total capacity of all resource buildings in all your nations.