I don't know how it is over the Pacific but when crossing the North Atlantic, aircrafts change from VHF to HF communications (more range). Depending on the exact route of the flight, several ground stations can give ATC assistance: Canarias, Gander, New York, Paramaribo, Piarco, Santa Maria and Shanwick for the South central part of the North Atlantic Ocean (from Ireland coast to New Foundland and from Canary Islands to Venezuela coast.
For the Pacific Ocean there are these ground stations:
Honolulu, S. Francisco (provides coverage for Anchorage), Guam, Hong Kong, Manila, Naha, Port Moresby, Seoul, Taipei, Tokyo, Auckland, Nandi, Pascua, Port Vila, Rarotonga, Sydney, Thaiti and Wallis.
I think there are no radar coverage over large portions of both the North Atlantic and Pacific.
Source: The worldwide aeronautical communications frequency directory, Robert E. Evans
Luis, Faro, Portugal