I want to buy the Kontakt 8 upgrade from Sweetwater. I am currently running Kontakt 7. Does the upgrade simply run right on top of Kontakt 7, or is it an entirely separate install (so that I would have both 7 and 8 on my system)?
You would have both Kontakt versions installed unless that you uninstalled version 7.
Mind you , if your DAW is able of doing this then the DAW should be able to auto-migrate projects but if the DAW/software can not then you can have both Kontakt versions installed at the same time though both what is saved in V.8 can not be opened in V.7 and some Kontakt libraries do require Kontakt 8.
Ref. : Notes about Auto-Migration of Kontakt Versions in DAW Projects
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If I uninstall Kontakt 7 before downloading and installing Kontakt 8, would that remove 3rd party Kontakt sound libraries? So I would simply have to find them again in my file system and re-install them into Kontakt 8?
I do not know enough about Kontakt migration , but @Jeremy_NI ought to know…
We would rather recommend to first install Kontakt 8, check everything is loading correctly then uninstall Kontakt 7. Actually you don't even have to uninstall Kontakt 7 completely, you just need to delete any plugin files from your DAW's plugin folders, as explained in the article.
It does not matter much anyway, you install the Kontakt libraries in Native Access, once you open Kontakt 7 or Kontakt 8 it finds the libraries automatically.