Rollout isn't necessary for CAT IIIB.
Requirements are that the runway is equipped and approved - it needs an ILS with self monitoring and standy power supplies.
The aircraft needs to be equipped and approved - installations vary wildly, esp with older aircaft but basically the system uses two or three autopilots ( or single multi-channel) to couple to the ILS. Below a specific height (not altitude) the a/p uses rad alt (a misnomer) to determine closure rate and effect a flare. The aircraft either has rollout which uses the rudder to steer along the localiser beam or at the point the wheels are down you disconnect and are on your own. Most a/c use autothrottle for autoland, on some it's mandatory some don't need it. The reliabilaty, trustworthiness and ease of use vary wildly from type to type. On 757/767 the system was fairly trap free and a joy to use. On the 747 classics I flew it was a living nightmare, and most people were pleased to pick up a CAT I downgraded a/c so you knew you wouldn't have to try!
The crew need to be trained to CAT II/III standard.
There are subtle differences between the US and Europe as to exact procedures which allow a continued approach.
Once you get out of Europe autoland capable runwys are thin on the ground.
This subject can get awful complex - both technically and wrt the rules. A minefield.