I don't know which one's bigger, the 777 or the A340, but one of the Saudi Prince's has a A340 which he uses extensively.
And about a year ago, there was a 747-400 being flown around by a private individual from overseas. I've also seen a couple 747SP's in the day - one was part of the royal family, and another was a big insurance company here in the US.
There's also a handful of 767 and a 777 or two out in the private sector right now. Sorry I don't have any information for you though.
--------------
Buttttttt.... while we're on the subject of the private aircraft. I was down in Dallas a couple weeks ago and was talking to one of the ladies who is a sales executive at one of the "private aircraft furnishing" facilities there. She said that typically they come empty from the factory, and they sit down with the customer and design a custom interior to suit their needs and style.
The figures she gave me though about made me jaw drop.
She said to outfit a new 737 BBJ runs typically in the $20-30 million range.
A new 777 (which they've done one of) ran over $80 million.
And a 747-400 which they were about to receive from an overseas country, was going to run in the $100-120 million range.
Another thing I found interesting was that she said the majority of the costs has to do with the paperwork, and certification tests and paperwork they have to do to get everything ready to go for the customer.
Amazing what some people spend on private aircraft!