I woke up to hot water running in my bathroom tub. Turning the faucet on and off did nothing to stop it. It was not running "full blast" but was a steady stream. The only way to stop it was to turn off the hot water tank. What would cause this? A malfunction in the faucet or is something else going on?

There is a problem with the faucet, possibly needs seats and washers or if it is the type that uses a cartridge then the cartridge need replacing.