If you are in a de-facto relationship or the spouse of an Australian citizen/Permanent Resident or eligible New Zealand citizen, you can apply for the Partner Visa (SC 820/801). You can only apply for this visa if you are in Australia. This visa allows you to stay and work in Australia indefinitely.
Partner Visa Process: After meeting the eligibility requirements for Partner Visa, the first step is to apply for Temporary Partner visa which is SC 820. If at the time of approval of SC 820, you have been in a long-term relationship with your partner (i.e 3 years or 2 years if you have a dependent child together), you will immediately be granted the Permanent Partner Visa which is SC 801. If you do not meet the long-term relationship criteria, you will have to wait till you complete 3 years (2 years with a dependent child) to be granted SC 801.
*Only under special circumstances, you may be eligible to apply for this visa even after your relationship has ended.