How do I remove the Ubuntu Software Center?
I believe the command you are looking for is
sudo apt-get remove software-center
None of these answers address the elephant in the room. software-center is a dependency of ubuntu-desktop. This isn't a major problem at first, until you run apt-get autoremove at some future date, removing all the other packages in ubuntu-desktop and making the system unusable.
To avoid this problem, you need to mark the other packages in ubuntu-desktop as manually-installed. Do the following:
sudo apt-get install alsa-base alsa-utils anacron at-spi2-core baobab bc ca-certificates checkbox-gui dmz-cursor-theme doc-base eog evince file-roller fonts-dejavu-core fonts-freefont-ttf foomatic-db-compressed-ppds gedit genisoimage ghostscript-x gnome-calculator gnome-font-viewer gnome-menus gnome-power-manager gnome-screenshot gnome-session-canberra gnome-system-log gnome-system-monitor gstreamer0.10-alsa gstreamer0.10-plugins-base-apps gstreamer0.10-pulseaudio gstreamer1.0-alsa gstreamer1.0-plugins-base-apps gstreamer1.0-pulseaudio gucharmap gvfs-bin inputattach language-selector-gnome libatk-adaptor libnotify-bin libpam-systemd libsasl2-modules libxp6 lightdm memtest86+ nautilus nautilus-sendto notify-osd openprinting-ppds printer-driver-pnm2ppa pulseaudio rfkill seahorse software-properties-gtk ssh-askpass-gnome system-config-printer-gnome ubuntu-artwork ubuntu-drivers-common ubuntu-extras-keyring ubuntu-release-upgrader-gtk ubuntu-session ubuntu-settings ubuntu-sounds ubuntu-sso-client-qt unity unity-control-center unity-greeter unity-settings-daemon unzip update-manager update-notifier wireless-tools wpasupplicant xdg-user-dirs xdg-user-dirs-gtk xdiagnose xkb-data xorg yelp zenity zip
sudo apt-get remove ubuntu-desktop software-center
The first lines marks all the contents of ubuntu-desktop (other than software-center) as manually-installed so that they won't be subject to autoremoval
That way, removing ubuntu-desktop will not mark the above packages as for removal.
Hope this helps. Like I said, the above methords "work" so long as you don't run apt-get autoremove at some point in the future.