Why does removing Firefox install another browser?

If uninstalling firefox installs epiphany, then that's because some other package depends on "a web browser", which packages do by depending on the virtual package www-browser. If the google-chrome package doesn't have a Provides: www-browser line, and you have no other browser installed, APT thinks it needs to install a package that does provide a www-browser and then Epiphany is the first choice on a GNOME system.

I downloaded one of the Google Chrome .deb files and I can confirm that they don't provide www-browser. If you want to get this fixed you need to file a bug report with Google and tell them to fix their .deb packages.

Removing Firefox does not install or uninstall epiphany-browser. I couldn't reproduce your problem, but there is no need for adding a wildcard after firefox in your command.

Instead of using:

sudo apt-get purge firefox*

Use:

sudo apt-get purge firefox

This command will take care of removing all Firefox packages. If you are still having troubles, then please post the terminal output when you try to remove Firefox, so we can see which packages are being removed.

BTW, the purge command has the same effect as remove, since Firefox does not store any config files in /etc. If you want to remove personal Firefox settings, you need to manually remove the folder ~/.mozilla/firefox

To make Google Chrome your default browser, run Google Chrome, open up Preferences and then under the tab "Basics" you'll find "Make Google Chrome my default browser". Click that button.

You don't need to uninstall Firefox.