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If the fans are staying on it's almost surely because of a stuck relay. There are three relays that control the cooling fans and they are located on the back of the shroud at the bottom.
The relays switch power on and off to the fans on command of the engine controller (PCM). They receive a constant power feed all the time on one terminal.
What can happen is when a relay engages it can arc and weld the contacts together so power will still flow through the relay even after the coil that engages it turns off. This will keep power applied to the fans unless the battery is unhooked.