can I install Windows 8.1 Pro OS on a USB hard drive or USB memory stick so as to be able to use on any desktop that allows boot from USB and masking of the regular HD ?

no, this is not possible

Windows - even the oldest one = Windows 95 - was bound to the specific
hardware of the pc where it was installed to. Therefore it even wouldnt
work with a standard harddisk to switch from pc to pc.

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Hi Falther:

Many thanks for your concise & comprehensive reply.

Sorry @Falther.. but we aren't in 1995 anymore!

well tell this to Microsoft then:

http://www.microsoft.com/en-us/windows/enterprise/products-and-technologies/devices/windowstogo.aspx

@HaQue

The question was for Windows 8.1 Pro

Your link referrs to Windows 8.1 Enterprise

Furthermore I doubt that this solution is able to cover new hardware
- i.e. one has to wait for an online update - if there is an internet
connection available at all ... and if the ethernet card driver is installed
... and if not .... a W-Lan connection is available and one has access
(password) for it.

I bet it will work on computers with old(er) hardware where all drivers
are included in the Windows respectively at least the (W-)lan drivers
are included to have an internet connection.

How much is the price for the Windows 8.1 Enterprise ?

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ah, ok, yes it isn't quite what the OP wanted. I haven't actually used that stuff either so I don't know how useful it really is. I don't know if the actual version would matter for the OP, maybe he hasn't looked in to the feature set to see if another version would do.

I don't know the price, but probably would be significant. Also there looks like a few caveats - certified drives only("A Windows To Go image running Windows 8.1 is capable of booting from a drive that contains a built-in smart card"), specific hardware and such, and I bet it really takes a companies IT dept to set it up properly.

anyway probably not a good answer for this thread, sorry for the lighthearted jab Falther! interesting direction for MS tho.