Even though the marriage declared a nullity, both parents will continue to maintain their parental rights and obligations. The court will likely hold a separate hearing to determine custody and address issues of child support and visitation. These issues will be handled exactly as in a divorce case.
Property distribution will work much the same way as it does in a divorce action with the exception that the court will typically look to return the parties to where they were before the marriage (to the extent that it can).
Remember that the annulment erases a marriage so, theoretically, there should not be any “marital property” to split. Of course, this is not always realistic so the court will rely on its usual property division procedures – either equitable distribution or division under community property law – however, it will not address earning potentials and other “future” incomes.
The sole purpose of the court will be to restore the parties to their “separate” selves. Any actual community property such as a marital home or joint bank account will be split according to standard property distribution procedures of your state.