Books I keep deleting keep syncing to my library. How to delete them?

It's a CloudSync problem. I had the same problem and after much trial and error managed to delete them by going into My digital editions in documents in my computer and going into the CloudSync folder and deleting the files there. Then going back into ADE and removing the eBook from there. Close the ADE and hopefully when you reopen it, the reappearing books should be gone. Another way to do this is to right click on the unwanted book in ADE. Go into item info. Where it says location, click on the arrow which takes you to the documents file in your computer and highlights the unwanted book. Short cut is go into  Open in explorer instead of item info ( it's the next one down the list). This takes you to documents/CloudSync folder and highlights the file of the problem book. Delete the file. Go into ADE and remove the book. Close ADE and you might be lucky and find the book is gone. It is clearly a CloudSync problem and Adobe must have changed something in their systems as my problem with this happened in the same week as yours and I had been using ADE for over a year with no problems until now.

I have exactly the same problem and Adobe help says they do not support my device and sent me to this community site. No help at all. Interesting to hear someone else has the same problem at exactly the same time I have encountered the problem. What has Adobe done?