How to prevent system applications (like the Software Center) from asking for password?

Ubuntu Software Center authorization uses policy kit. When requested for the authentication during the remove action you can expand the "Details" pointer to see the action that is being invoked. It's org.debian.apt.install-or-remove-packages . You can change the corresponding policy to not request for authentication:

Edit /usr/share/polkit-1/actions/org.debian.apt.policy, search for org.debian.apt.install-or-remove-packages, then find for the defaults section, replace auth_admin and auth_admin_keep with yes .