He asked when someone else rights off your car, under the law you are entitled to the FULL replacement cost of your vehicle, however it's not always that simple to get the money.
If you have comprehensive insurance then all you need do is hand it over to your insurance company and they go in to bat for you, to either reclaim the expensive from the offending party's insurance company, or from their personal estate if they were uninsured or not covered (e.g. drink driving voids insurance cover). The second often gets messy, people wanting to pay $10 a week, and often ends in the courts. One good thing to remember is even if someone is over 18 there are grounds to reclaim costs from their parents IF they are still living at home and at least partially dependant.
If you don't have comprehensive cover (i.e. 3rd Party), then some companies will look after you, others will leave you to fight the battle for yourself. If you have no insurance then you're all alone too. That means you have to get a letter of demand issued, etc, etc.
If you do get stuck alone you should really consider seeking legal advice because it's all too easy to get screwed by the other party or their insurance company.