1) Syncing syncs — it applies the changes you made on each device. It doesn't just pick a side and delete all other data. (You can manually use Replace Online Library from the Sync → Reset pane of the Zotero settings, but that's generally only necessary if you restored from a backup — say, from before some accidental deletions — and want to overwrite all other devices with the older version.)

2) In this case, it's not clear how the data got on the different computers. If it was done by using export/import, or by saving the same items from the web, these would be in effect unrelated items, and syncing now would result in duplicates.

3) Deleting the Zotero app has no effect on local data. If you reinstall it, you'll see the same data that was there before. So that won't work to prevent local data from being uploaded.

Generally speaking, if one computer has all the data you want and the others have other libraries (maybe made via export/import, maybe saved manually) you want to get rid of, you could just delete the Zotero data directory on those other computers. But if it's anything other than that, you'll need to explain further. (Specifically, I'm not sure what you mean re: PDFs. Are you saying the other computers have PDFs that need to be kept? How were those libraries created, and how do they relate to the library on Computer A?)

Thanks a lot, dstillman.

2) by saving different or partially the same items from the web to different computers.

Thanks for the explanation. So, the best way is to remove the Zotero data directory from Comp. B and C., and synchronize with the most recent data uploaded from Comp. A. It works if there is nothing to be kept (from Comp. B and C), otherwise, there will be duplicates, right?

I think the patron used different computers parallel without synchronizing, and now he would like to unify the data on all of them.

Yes, if there’s nothing to be kept, deleting the B and C data directories is the best option.

If the amount of overlap is minimal, the alternative would be to just sync all three and use duplicate detection to merge some items, but beyond a small number of duplicate items that would get tedious.