Although I linked to that particular article, there are other news organisations that have asked the same questions about Australia's Over the Horizon Radar, including Bloomberg.
UK, AUS, NZ , Canadian and US intelligence surveillance systems are pretty much run as one system, centralized and guided by the US.
The US/Australian OTH radar is a joint operation and therefore it wouldn't even be a case of the Australian "handing over" information. As with GCHQ, this kind of intel is live streamed and patched into the US's global surveillance system.
Australia's OTH radar is not switched on or pointed in any direction, it is on permanently and covers the entire area as shown on the map I posted. One of its prime uses is as a missile defense detector and will track any moving object within its zone of detection.This zone of detection goes out at least 3000 km from the coastline of Australia, and most defence anaylists agree probably quite a bit more.
A large commercial airliner flying within this zone would automatically be detected, especially if it is flying over open water.