QUESTION - Range and Accuracy

[Bob C]

My understanding is that ADSB/ModeS systems detect aircraft within about a 250km-350km range.

If this is correct, how can sites such as FlightRadar24 and PlaneFinder show flights hundreds/thousands of kms from nowhere over Central Australia and the Pacific and Atlantic Oceans ?

For instance , I just noticed several ANZ flights tracking south-west a long way south of Hawaii on their way to Auckland, so how can these be shown ?