Here's the typical route for the Atlanta to Johannesburg flight I do once in a while:
http://flightaware.com/live/flight/DAL200 As you can see, it is out over water, well away from any radar coverage, or VHF radio coverage, for 90% of the flight. Luckily (for me) most of the way we do have Satellite comm via CPDLC with various controllers along the way, starting with NYC, then Santa Maria, then Abidjan, Dakar, Windhoek, and finally Joburg.
We use HF as a back up, but we have zero radar coverage most of the way, only over land in the US and in Africa.
Here's the track for a typical ATL-Dubai flight, I just flew this a few days ago.
http://flightaware.com/live/flight/DAL8/history/20140313/0150Z/KATL/OMDB As you can see, you have much better radar coverage because you are over land much more, only out of radar contact up over the north Atlantic for about four hours. We have CPDLC the entire way over water there however, and also use HF for back up. Over land, we use VHF most of the time, unless we are wayyy up into Canada going on a Polar route, to say Shanghi out of Detroit.
http://flightaware.com/live/flight/DAL583/history/20140313/1720Z/KDTW/ZSPD We go straight north out of Detroit, over the north pole, and down the back side, so we have no radar and no VHF and even the HF won't work too good up north of 72 degrees north. Sat com works most of the time up there though, which is nice!
Here's the Tokyo to Singapore route I used to fly quite a bit, as you can see, they put an Airbus A330 on the route lately, so I'm not flying there any more, but it may come back to the 777 in the summer. You can see it's over water a lot more than over land, and we are out of radar coverage quite a bit, and using CPCLC most of the time for communications with ATC.
http://flightaware.com/live/flight/DAL621/history/20140313/0900Z/RJAA/WSSS We really need to get the third world to buy into sat-com and get better coverage, and stop using HF. Also, Radar has limitations out over water, because it has to be physically mounted to something, ie. a land mass, or a ship, and it has limited range. I doubt any third world country is going to spend the money to put a ship on station just to monitor airline traffic.
