The opening poster asked about the "investigation." Logically it belongs to Malaysia.
Search and rescue belongs to us, however we are happy to have help.
This was a Search and Rescue; the search in terms of SAR is complete and there will be no rescue, so Australia's responsibilities have ended.
I never suggested we shouldn't search and I don't agree with the chestnut that the planes were airborne anyway. Perhaps a ship or two or maybe one plane may have been up or out, but not 90% of our airborne RAAF SAR fleet.