schleprock,
CATIIIA approaches are at no ceiling with 50ft DH
CATIIB have no ceiling and 17ft DH
CATIIIC would have no ceiling and 0 DH, but as far as I know they are not flown until now due to the lack of suitable airborne equipment.
Autoland is not always needed for cat III approaches. The Canadair Ragiional Jet is certified to fly CATIIIA appīs without autothrust and with a head up guidance system. For B & C autoland is mandatory. It consists of Autopilot and autothrust. The Autopilot must be able to perform an automatic flare. As far as I know, for CATIIIB also an auto-rollout feature is needed.