How airplanes of new generation communicate with ATC over remote areas? (North Atlantic Region)
Planes in the North Atlantic with the latest equipment as you ask would use VDL only within line-of-sight. Otherwise they would use satcom or HFDL (HF data link) for data comms.

(Click for full map) VHF coverage for FL 300, the lower the plane, the smaller the areas.

Data communications will be via CPDLC or ACARS. For voice communications there is also a satcom voice option. There is also ADS-C for tracking, which is mandatory for certain flight levels.

Pilot-to-pilot voice communications to relay information or during emergency is also available on 123.45 and 121.5.



Further reading and source: ICAO NORTH ATLANTIC OPERATIONS AND AIRSPACE MANUAL