Final answer:
The Department likely has 'full authority' over the files from each Board, aligning with governmental structures where departments control and regulate their areas, including the appointment and dismissal of officials.
Step-by-step explanation:
The sentence to be completed is: 'The Department has ______________ over the files from each Board'. The most appropriate completion from the given options is 'full authority'. This phrase aligns with the context of a department within a government system having control over the documents and proceedings of its subsidiary entities, reflecting the centralization of power. In historical and contemporary terms, governmental bodies often have full authority to administer and regulate their areas of responsibility, which is indeed the essence of an executive department or agency.
This authority extends not only to overseeing the proper functioning of departments but also the rights to appoint and dismiss officials as necessary, and to ensure adherence to governmental rules and regulations, indicating a hierarchy where local bodies execute the central government's directions.