Steve
You're pretty well there. Take a typical Heathrow-Kennedy flight routing via Shanwick into Gander:
Approx 30-90 minutes before entering the Shanwick Oceanic Control Area the flight will request an Oceanic Clearance. (Shanwick, as with other OCAs, is Class A Airspace above FL55 therefore an ATC clearance is a requirement - with few, usually military, exceptions). The clearance would be requested/issued on a Shanwick Control (Prestwick) VHF frequency or by using an ACARS based system called ORCA. ('Oceanic Route Clearance Authorisation'). If required, a clearance can also be requested/issued via Shanwick Radio (Ballygirreen) on HF.
The requested/cleared route will be either on what is called a 'Random Route' or alternatively follow one of the designated tracks of the North Atlantic (NAT) Organised Track Structure (OTS). The clearance will apply from the Oceanic Entry Point all the way across the ocean to a designated Landfall which falls within a radar environment
Once in receipt of the clearance the flight will arrange to cross the Oceanic Entry Point at a specified time (give or take a couple of minutes) and continue in accordance with the FL, route and speed contained in the clearance, until again coming back into radar cover in a Canadian radar sector. (Changes whilst en-route to the cleared FL, route or speed can be requested by crews at any time however).
Once within the procedural (non-radar) environment of the OCA, ATC plots aircraft positions using actual and estimated times over significant points held on the route, speed calculations taking into account the forcast MET and ensures that safety is maintained by applying horizontal separations which are so large as to make your average radar controller green with envy. (Or cry in despair - one or other!). Vertical separation remains at 1000' up to and including FL410. (Unless you're an A380, in which case you get 2000' between you and the next guy below!)
Communications with ATC are via HF or CPDLC ('Controller-Pilot-Data-Link-Communications') and the flight will make routine Waypoint Position Reports either again via HF or by using ADS at every significant point along the cleared route. (Usually every 10 degrees of Longitude). Once within the Gander OCA the flight will then fall under their jurisdiction and Gander Radio will handle all HF comms and Gander Center the control function.
Oceanic flight data is held in much the same way as flight data at any other ATC centre, although the procedural control aspect makes Oceanic Control a fairly unique ATC environment. (The technology used also being quite different from your typical en-route ATC radar-based centre).
Hope that clarifies things
