From 1940 immigration came under federal government control. Information for arrivals from this time is available in a number of resources, the most comprehensive records are held by the National Archives of Australia, covering the period up to 1989.
The National Archives Passenger arrival lists 1897-1966 are searchable online.
Information for later arrivals can be obtained by applying to the National Archives.
The South Australian Maritime Museum has compiled the Passengers in History database recording 328,000 arrivals in SA between 1836 and 1964. It also includes references to individual ships' voyages from the Log of Logs publications.