WHAT IT WAS!
I sent a picture of that thing to "Seabart," the web master of www.uglyships.com, and asked about it. Here's his reply:
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What you saw in Stavanger is not a drill ship but a so-called FPSO: a Floating Production, Storage and Offloading unit. Designed to be anchored above a small oil or gas well that's not producing enough to warrant a complete platform with pipelines to the shore or maybe too far away to install a pipeline to the shore.
The derrick on the stern is a so-called "flare" where natural gas that cannot be processed or sold is burned off. The oil is pumped up, cleaned etc and stored on board of the vessel until a shuttletanker stops by to transport the oil to the refinery ashore. The notation 15/12 Talisman is the name and number of the actual well.
And yes: it's an ugly thing. Good thing that they are usually moored far, far, far away offshore so you (usually) don't see them from the shore.