When you say 'outside territorial waters (over 12 miles) does this mean that no one really has authority over the Atlantic once you get more than 12 miles out then ?
It's actually a bit more complicated than that. Extra-territorial waters while not actually being under direct control of any government are not the be thought of as no-man's land. There are international treaties dealing with what happens beyond the 12-mile limit. A prime example is the case of the two Italian Navy officers who are currently standing trial for having allegedly shot at an Indian merchant vessel killing some Indian seamen. Although this clearly happened in extra-territorial water and they are members of a foreign military force, they will still stand trial in India because a court has decided that the event falls under their jurisdiction.
And then there are the rogue countries like North Korea that have decided to set their own (much wider) boundary and to deal accordingly with "intruding" foreign vessels. In that case if engaged there is nothing you can do, short of returning fire, to escape capture. The North Koreans are not known for being particularly reasonable people.