Any one know how to remove this shared chrome instance?

Solution 1:

This is part of the handoff functionality. Which is indeed linked to an AppleID. You can easily disable handoff in System Preferences.

System Preferences --> General 

And then uncheck “Allow Handoff Between This Mac and Your iCloud Devices”.

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More info on handoff at the Apple's website Pick up where you left off with Handoff on Mac.