I don't believe capitalism will 'die' per say, just change a lot to the point that we may not recognize it. There's a belief that capitalism is a recent invention, and to some extent it is, but at the same time the notion of buying/selling based on supply and demand and markets have existed for ages. Some form of the notion of supply and demand and exchange of value will continue. I do believe some notion of markets and supply/demand will continue to exist in the future, and will probably be how any form of automation does resource allocation/prioritization.
What will almost certainly change is the notion that people need to work to earn money. The reason is pretty simple: there's going to be more people than there are jobs to do. For the next few decades or so, automation won't replace highly skilled jobs, but automation will certainly replace things like manufacturing, truck driving, ships, aircraft, taxis, etc. We're already seeing a large number of these jobs being replaced now. Sure these systems will require maintenance from time to time, but we won't need the sheer numbers of manpower we needed before: otherwise it would be somewhat pointless to replace humans with machines if the machines were just going to cause the same amount of problems, just different problems. The highly skilled labor associated with software, robotics, etc. will probably be around for some time longer. Eventually they too will be replaced, or at least, minimized to the point that not many are needed. What we'd be at at that point is a society that doesn't have as much work to do.
This isn't to say that there won't be problems to solve. On the contrary, the problems to solve will just change and become more complex. There's a book I'm currently reading, called The Inevitable, by Kevin Kelly, and it deals with these sort of things discussed here in this thread. Take understanding gravity, (just as an example), or complex quantum physics. AI will help us solve these problems. Humans will still be needed, since basic AI still requires being put in a direction.
Now if we talk about true AI, that will exist at some point as well. It won't be human-like though. It'll be utterly alien to us. It won't think the way we do. It'll think very different from us.
Now for the scenarios. It's entirely possible that automation will lead to everyone being in mass poverty, save for some select people. It's a very Marxian scenario (Spontaneous World Wide Workers Revolution), but it could happen for a few reasons:
1): This is a really simple reason actually. What do people do without anything better to do? People without jobs, etc.? Sex. And that could lead to a population explosion that creates serious burdens on the system (assuming no one bothered to do something about birth control)
2): No one bothers about the people who are the losers of automation. We're already seeing this, to an extent in politics, becoming a concern. I see this as a possibility, but I don't see this as likely, as beyond a point, a select few cannot fend off hordes of people.
3): Sentient AI rules us in a Matrix or Terminator scenario. Now this is incredibly far fetched, because it makes assumptions. It assumes that sentient AI would see us as hostile. The fact is that we don't even know what sentient AI even looks like. We aren't even sure what sentient means. Sentient AI, in my opinion, would be extremely alien to us in its thought processes.
4): We blow the shit out of each other, and there's nothing left, save for automated stuff rationing out the remains. Ironically enough, this may actually be the most likely scenario out of all the ones I've listed here, simply because people just don't like one another a lot.
Then there's the utopian scenario where there's plenty for everyone. It could happen if:
1): People actually work together and don't kill each other.
2): People actually consider the effects of mass automation
3): People are willing to see capitalism change into something new
4): Sentient AI doesn't hate us
5): Some other cataclysmic event doesn't happen first (Ie, alien invasion, etc.)