Ubuntu – How to find the reverse dependency of a package?

In most cases the autoremove command of apt-get would do the trick, it will remove all packages installed and marked as automatically installed, but not required by any other installed package. This is the preferred and secure method when the master package is not a metapackage.

This is not the case for metapackages like kubuntu-desktop, and this is because packages installed as a consequence of the installation of a metapackage are not marked as automatically installed, so that cannot be remove by autoremove.

Removing all packages marked as dependences of, or recommended by a given metapackage, like kubuntu-desktop, could be dangerous, because some of those packages could be on your system before the installation of the metapackage.

The most secure method to proceed, in my opinion, is an analysis of /var/log/dpkg.log and its ancestors, to see which packages were installed in timestamps around the timestamp of the installation of the given offending package. I suggest a command to get a more terse and cleaned-up view of the concatenation of the involved log files:

less $(ls -rt /var/log/dpkg.log*) |
  awk '$3 ~ /^(install|upgrade|remove|purge)$/' |
  less

Try sudo apt-get install -f. It will probably give some suggestions about removing and installing packages, do what seems reasonable. If that doesn't help, try booting into recovery mode and choosing the "fix broken packages". If that doesn't work... I don't know, I'd reinstall Ubuntu if I were you. (This is a good reason to always have /home on a separate partition!)