borough, urban prefecture, govt office, representative body, storehouse
府 centers on a central administrative place: a government office, an urban prefecture, or a representative body. The storehouse sense extends this idea to a place where things are kept and managed.
府 combines 广 (building with a roof) with 付, which likely contributes the sound and the idea of attaching or administering. Together they suggest a place where official business is conducted or goods are stored.
Under the roof 广, an official 付 is attached to a government office, managing the borough and its storehouse.
For フ, imagine a government office with a huge 'fu' (like 'foo') stamp on every document: fu -> フ, marking the urban prefecture's authority.
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government; administration; ministry
(urban) prefecture (i.e. Osaka and Kyoto)
prefectures (of Japan); largest administrative divisions of Japan: Tokyo-to, Osaka-fu, Kyoto-fu, Hokkaido and the remaining prefectures
shogunate; bakufu
Kōfu (city in Yamanashi)
provincial capital (under the ritsuryō system); provincial office
prefectural police (Osaka or Kyoto)
prefectural governor (of Osaka or Kyoto)
realm of the dead; the other world; underworld
the government; Administration
prefectural resident (of Osaka or Kyoto)
prefectural; managed by an urban prefecture (Osaka or Kyoto)
assize; court
within the prefecture (of Kyoto or Osaka)
prefectures (of Japan, excl. Tokyo and Hokkaido)
Nationalist Government (of China; i.e. under the Kuomintang)
prefectures (of Japan, excl. Tokyo)
educational institution; academic centre; academic center
prefectural assembly member (in Osaka or Kyoto Prefectures)
prefectural assembly (in Kyoto or Osaka)