Having just qualified on the B744 and whilst still very wet behind the ears, I do know that the a/c is certified for flight with only three engines. There is no mention in the QRH of any requirement to land as soon as possible if you shut one down and no doubt the operating crew will take this as well as all other factors into account before deciding whether to continue or not.
There seems to be some confusion, especially by those who have not flown the B744, about what it is certified to do and what not. In this case, the crew elected to shut down the engine. There was no catastrophic failure. All other systems would have operated normally, including all 4 (four) hydraulic systems and 3 (three) packs. I assume their maintrol would have had access to more data than the crew about the health of the engines through the ACARS links.
Criticism of the crew by those who would not have made the same decision to continue is fine if you are not only familiar on the type but also experienced. Anyone else making a comment should first realise that without experience on type (and I mean the B744 and not just other tri-engine types or A340 which have different systems) they are assuming that the crew didn't have any regard to their own or their passengers safety which is most certainly not true.
What is the ATC call when a quad becomes a trike? Pan or Mayday?
Neither. As has been mentioned the a/c is certified to fly on three engines should one be shut down after take-off. And before the nit-pickers jump on my case, I know that three-engine ferrying is a separate issue.
All reference to ETOPS and twins is irrelevant to this case and the debate about whether 180 or 207 minutes certification for twins is safe should be carried out elsewhere. The references to the FAR's as pointed out are obviously ambiguous and allow the commander enough discretion to use his or her common sense, experience, training etc. to make the necessary decision. I think the bit that says;
"...he decides that proceeding to that airport is as safe as landing at the nearest suitable airport" is the get-out clause and the FAA probably don't have much to stand on. If the a/c is
certified to fly on three engines then there is no reason why landing at
'that' airport is less safe than landing at the
'nearest' airport.