According to the Australian Bureau of Statistics there were 823,254 sole parent families in Australia in 2006 up from 649,000 in 1996.
Around 87% of sole parent families are headed by mothers. This figure is changing, with more single fathers now becoming primary carers of their children. According to the Australian Bureau of Statistics sole fathers are more likely to care fore teenage children.
The Social Policy Research Centre at the University of NSW conducts a lot of research about families, including sole parents, as does the Australian Demographic & Social Research Institute at the Australian National University.
Bryan Rodgers and Jan Pryor have done extensive research into the effects of divorce on children, including the excellent Children in Changing Families: Life after Parental Separation. They look at separation and divorce as a process, not an incident isolated from everything else. That is, separations don't just happen by themselves. They generally come after a long period of being unhappy and in conflict, and it is the whole process, not just the one incident, that can be difficult
The Australian Institute of Family Studies is another authoritative source. Their Family Matters Magazine is published twice a year.
For information on who pays how much child support, the Child Support Agency's Facts and Figures are published annually. Key figures from the 2008/09 Facts & Figures are:
Centrelink provides limited information on their customer base, and may be able to provide additional information on request. Of course, as with all government agencies they must respect the privacy of their clients.
The Family Court publishes information on the outcomes of its decisions. Download copies of their latest research here:
Family Court Public Interest Statistics
Shared Parental Responsibility Statistics