So what do you do? If you have an Android device (in principle, you could use an Android emulator as well), you can download the NOOK e-reader Android app and, through a few steps, get the same ePubs you used to download. Here's how you do it:
- Download and install the NOOK e-reader Android app on your Android device
- Open the NOOK e-reader app and find your library with your newly purchased book
- Select "Download" to cache the book locally on the device, and wait for the download to finish
- Once the download is finished, open a file manager application like ES File Explorer and navigate to
/sdcard/Nook/content
You should find your NOOK book ePubs in that folder. That is, find the Nook folder in your internal storage, and then find the content folder inside it. - You can use your file manager to copy those ePubs out of that folder, or you can "Share" them to another installed app like Dropbox or Google Drive so that you can easily get them on other devices or your Desktop computer
[ Side note: You might try to plug your Android device into your computer and use MTP to access /sdcard/Nook/content directly from your Desktop and copy files out of it. However, it's possible that the ePubs won't be accessible this way. In fact, the might not even show up in the file listing. So you might be stuck using a file manager on your device. ]