What is drilling in the Falklands is called a semi-submersible drilling rig, the one they are using is the Ocean Princess. Its not much of a princess and last time I worked on it about 15 years ago it was a right old sh1t heap. They are towed by a couple of supply boats or tugs and anchored to the bottom while drilling.
The picture up the page is of a newer generation of directionally possitioned semi's that are used mainly in deep water – just like the one that sank in the gulf a couple of weeks ago. They dont use anchors as they are self propelled (most of the time)