The Law of the Sea

With the increase in pirate attacks off Somalia, or at least an increase in news coverage of the attacks, a couple of questions regarding international boundaries come to mind. Are the oceans and seas all part of one country or anothers territory? If there is no central government, is a country really a country?
From the United Nations we have the Law of the Sea Convention.
For an understanding of Somalia see the country description at the U.S. State Department's Somalia page.