VIC Permanent Residency and Custody of Children for Illegal Immigrant?

[MissSomeone]

Hi, I just wanted to know if a person was in Australia illegally with no visa or sponsorship can get got shared custody of children. Is it possible for the person to apply for permanent residency in Australia and stay in Australia permanently?

 

[AllForHer]

This is a question for Immigration, rather than Family Law. I am aware that parents have been deported due to being illegal immigrants, even if their child is an Australian citizen.