One thing I wanted to add to what Mr. Giaschi said earlier is that it's important to note that not only do these conventions provide a limited liability, but they also specify who pays for the cleanup. It says that the seafarer does not pay for the cleanup, and it specifies who does. In the case of a convention vessel carrying a persistent or crude oil, that comes from a high deductible paid by the shipowner, first. The rest of the money comes from the international oil cleanup fund.
On April 30th, 2009. See this statement in context.