Microsoft says in their tutorial on upgrading to 8.1 Under Prepare Your PC:
"Connect to the Internet. It's not required, but we recommend that you stay connected until the update is done. If you don't, youll need to connect again to finish setting up later, and setup will take longer."
Probably, the real reason they say the above is so that you will need to create a Microsoft account (if you don't look extremely carefully and see where to click to get to a local user account). So, after you get the update downloaded from the Microsoft Store simply DISCONNECT. Then the installer will not be able to talk to Microsoft during the install and setup and will simply offer you a local user account. I have not yet upgraded to 8.1 so I am not sure it will work, but a Google search shows this being recommended by many sites. So, it is certainly worth a try.
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social.technet.microsoft ··· ogeneralIf you don't want to try the above (or it doesn't work) then after the first phase of the upgrade is complete, your computer will reboot and the second phase begins where you choose your settings. Microsoft says that when you get to the Sign in Window
if you want to use your local account from Windows 8.0:"To keep using a local account
Windows 8.1 is designed to be used with a Microsoft account, so we recommend that you give it a try. Simply put, your Microsoft account is the glue that holds together so many useful features of the new Windows. Without one, you won't be able to, for example, automatically sync your settings and documents between PCs, back up your photos to the cloud so you can get to them from anywhere, or see all your contacts from multiple email and social networking accounts together in the People and Mail apps.
But if you're sure you want to use a local account instead, choose Create a new account, and then on the new account page, choose Continue using my existing account."
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windows.microsoft.com/en ··· ial#know