Are desktop PCs and laptop type computers being replaced by tablets and smartphones?

To some extent, yes, as indicated by the shrinking volume of desktop pc's for a long time, and growth in the tablets and smart phones, and a highly competitive laptop market where Samsung has left the laptop market pretty much, and Sony has also. The new ultrabook designator, owned by Intel, now refers to convertible laptops. Tablets with docking keyboards are around. Windows 8 is tablet oriented and is a failure in a clamshell design.

There's still a place for each though, and nothing will disappear for a long time.
The CPUs in even tablets is limited and graphics performance even more. Any serious gaming takes a tower PC. Tower PCs were still increasing in volume in developing countries until laptops dropped further and further in cost to produce and therefore selling price. Lenovo passed HP-Compaq in the personal computer market volume because of Desktop PCs in China.
Tablets have an unprotected LCD and some people always want the keyboard of a laptop and its protective cover clamshell design. Not everyone favors touchscreens putting dirty fingerprints on the LCD all the time. When a person wants a screen at 21 inches, that is a workstation arrangement anyway, and various form factors are not an issue.

So, there will be a place for each for a long time, and instead, think of it as a market of expanding configurations.

Smart phones, tablets, convertible and docking and flip-displays, standard clamshell, small desktop units, all-in-ones, large size towers with glowing LED lighting and graphics and CPU performance that only 5 years ago was totally out of reach of consumers. There are wrist computers and eyeglasses with computer displays. We're not far off from holographic image 3D shown in science fiction in a room full of computers that can be done with a tower and projector.

Rather than replaced, how about supplemented, and volumes among them varying.

Tablet's aren't replacing PC Laptops and Desktops, It's the smartphone's that are replacing the Tablets. They're a more compact device, and have grown and evolved to a point of doing basically everything a computer can do (minus the ability of playing PC/Mac Games and having support for all those files), but give it some time and it may or probably will be able to. Think of it in the near future, as a pocket computer. It's heading towards that direction, but in no cases are Tablet's replacing computers.

Yes, most likely in the future (next 20 years or so) computers will be tiny, like phones and tablets. There will still be laptops and desktops but phones and tablets will be much more popular. Since this is already happening, it's safe to say that this will continue on in the future.

Not completely. For a programmer for e.g. A desktop or a laptop has multiple software(For e.g.NET Framework) to do coding, testing, deployment, etc. These can't be done on a tablet or a smartphone.
What tablets and smart phones replace essentially is the entertainment(music, games), file storage and maintenance(important documents, image files), audio/video chats(skype etc).

More supplemented than replaced. If you need power you need a desktop. When tablets and phones can compete with a desktop's speed and storage it may be different.