When you're divorced and still have to live together

Sometimes the marriage is over, but the financial ties to a house still remain. What happens when you and your spouse have divorced but must still live in the same house together? Is it possible to cohabitate without hostility? Can the children handle a broken marriage, where both parties may in fact be seeing other people? Can you really establish a new relationship and still be living with your ex-spouse? Or is this an indication that both parties have become too co-dependent to separate?