A320:
On CAT I ILS: A/P has to be disengaged at
80 feet with CAT 2 or 3 displayed in FMA
160 feet with CAT 1 displayed in FMA
On CAT II ILS: Minimum DH for autoland is
100 feet with at least one AP engaged in APPR mode and CAT2, CAT3 SINGLE or CAT3 DUAL displayed in FMA
On CAT III ILS: fail passive AL, Minimum is
50 feet with at least one AP engaged in APPR mode and CAT2, CAT3 SINGLE or CAT3 DUAL displayed in FMA
On CAT III ILS: fail operational AL
Alert height 100 feet (200 on A330)
Minimum DH for CAT III with DH : 20 feet (15 on A330)
Minimum DH for CAT III without DH: No DH
2 AP engaged in APPR mode and CAT 3 DUAL is displayed on FMA.
P.S. The CAT display on the FMA has nothing to do with the ground installation. It only reflects the current system capability.