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How to completely remove desktop?

So, I thought I managed to remove KDE completely, but apparently that did not work at all, because every KDE application is back, including the KDE splash screen.

I ran

sudo apt-get autoremove --purge kubuntu-desktop

Then I ran

sudo apt-get install --reinstall ubuntu-desktop

Then I ran

sudo sudo update-alternatives --config default.plymouth

Then I rebooted and everything seemed to be the original ubuntu-desktop (without the kde splash screen and other KDE applications). But now, one week later I still boot to ubuntu-desktop, but like I said, the kde splash screen and applications are all back.

How should I remove kubuntu-desktop?