An app downloaded from the Mac App Store re-installs itself after I delete it. How can I remove it permanently?
Some troubleshooting tips:


Open the Mac App store and choose the menu Store > Sign Out
Log out of your account (save work and then choose the menu Apple > Log Out ...
Log in and hold the shift (this prevents apps from automatically starting. If you miss the timing, just continue - things will be slower as a result)
Disconnect any network cables and turn off WiFi
Restart your Mac (Apple Menu > Restart)


At this point, you've disabled the checks and tools the app store will use to try and continue a download.

Open Launchpad and delete any copies of that app (and any others you wish to clean up).

Once that's done, restart your Mac.


Reconnect WiFi and network
Open the Mac App Store
Sign in again
Check for Unfinished Downloads (under the Sign in option)


At that point, you should be save from further intrusion of the App Store.

There's some great information on the tools here:


App Store repeatedly asking me to update