Are there any single major companies that owns the backbone? And Submarine cables?
Crown Fibre Holdings owns the new fibre network (I think Chorus owns all the copper, not sure) but Chorus manages most of it (by contract); Chorus is a crown partner company, and they are regulated and forbidden from certain activities - they were split off from Telecom, a private company.
I don't know enough about the backbone to usefully comment, except that there are at least 3 fibre networks running along the major road I live near.
For a long time there was only one submarine cable with any serious bandwidth (Southern Cross Cable), but aparently according to Wikipedia a new one to AUS was rolled out in March 2017 and another one to Hawaii this month.