A world without work...

As you can see, one of my hobbies is economics (it takes all kinds...). So, one of my favorite Gedankenexperimenten (it sounds so much better in German, even though I have no idea if the plural is correct) is to imagine a world where computers have all the jobs. And I mean all the jobs (from collecting fruit to administering justice), so people can just use their leisure time for whatever they want, as the greek citizens did (of course, in ancient Greece, for every Aristotle there were thousands of slaves). I don't mean a world after 29th August 1997, 2:14 a.m., where Google^H^H^H^H Skynet becomes self-aware, but a kind, gentle version where a computer takes care of all the needs.
What happens if scarcity is still around (and it will, no matter how much machines produce there won't be two Mona Lisas)? How do we assign economic capacity? Should we live in a communist state, where a computer decides how much each good is worth, and how much each person can have?
And what happens if there are still some disgusting jobs that still have to be done by humans (i.e., garbage collectors)? How do we compensate this poor individuals who have to perform such disgusting task? Or do we have a draft where everybody should do this for one year? And what about people who are willing to sacrifice some goods in order to avoid this draft (certainly, some people may consider that extra goods are worthy doing this jobs for a couple of extra months, and from there, it is just a question of supply and demand)
Comments are welcome

PS: After my small typo (I swear I meant Skynet!), further posts will be written clandestinely, since only this strange guy with a funny accent who says he will be the governor of California stands between me and a certain death by a liquid metal terminator.