I don't think the pc will ever die. I think that one day tablets will work alongside the pc in a cloud type environment. So you will be able to use a tablet for day to day uses, and anything that requires extra power will (gaming, scientific purposes, ect) will tap the computing power from a pc through the internet at your home, or servers that you rent, like a remote deskop almost, except you won't notice the change, it will just happen automatically. IMO clouds will always be hybrid systems, so I think pc's will always have a place. Just in the future they will be 1000 times more powerful than today. But we will always need more and more computing power. I see the pc as the central nervous system of our homes, and tablets are extentions of that system. I realize that in 20 years tablets will be way more powerful then the best desktops of today, but the applications will also require vast's amount of computing power. Video games will be like the matrix where you will wirelessly plug in with your wireless brain implant, and it will run off your home pc super computer holodeck style. And people will probably be building battle bots by then, and doing battle simulations on networks in which the more powerful systems will have advantages over weaker systems. The thing most people forget is that applications grow in requirements as technology gets better. So while you will be able to do a lot more on tablets in the future, there will always be apps that will require more and more computing power, and anyone who has the extra computing power will have an advantage when it comes to doing computing applications. Computing power = more ability = time saved.
Also, I think AI will require vast's amount of computing power, and since most people in the future will have robots, the more powerful your pc, the more the AI can tap into. One day we will all have "watson" type computers.