Re: The human pilots just do the easy bits...
So far as I know there is no fully automated take-off.
As for fully automated landings there are however very strict rules before a airport, plane and crew are allowed to facilitate or execute a fully automated landing in fog or general bad visibility conditions. Under normal visibility landing is not automated, if one of the minimal two autopilots fails landing can not be fully automated etc.
As for the comment by Airbus, interesting bit is that even if the pilot takes manual control it's still a computer (partially) flying the plane because of the fly-by-wire system, Boeing planes at least have a "very heavy" according to a airline captain (friend of mine) back-up cable system which fully works on manual aka crew power to move the control services.