Upon closing the last notebook Mathematica opens the notebook file
MathematicaNavigatorTrial.nb (if you are using a trial version) or
MathematicaNavigatorStudent.nb (if you are using a student version). These files reside in
[prefix]/Wolfram/Mathematica/8.0/SystemFiles/FrontEnd/TextResources. That path name is hardcoded into the Mathematica binary. If Mathematica really doesn't have an option to disable the welcome screen completely (it likely doesn't), the only solution I see is to modify the contents of
MathematicaNavigator.nb to make it exit Mathematica immediately. Before proceeding with modifying that file, be sure to disable the display of the welcome screen at startup time.
After you have disabled the welcome screen at startup, either by unchecking "Show at startup" checkbox on the startup screen or by using
Edit | Preferences | System | Show at startup -> New document, back up the existing
MathematicaNavigator.nb in case something goes wrong. Delete all code from
MathematicaNavigator.nb and replace it with the following:
Cell["", "", CellDynamicExpression :>
Basically, this represents a notebook with an empty cell having a dynamic handler. It activates when the cell is displayed to user. The handler
FrontEndTokenExecute["FrontEndQuit"] just sends the Mathematica FrontEnd a quit message, just as if you had given the
Ctrl+Q shortcut. By the way, calling
NotebookClose instead of
FrontEndTokenExecute["FrontEndQuit"] will always crash Mathematica with SIGSEGV on my machine (Mathematica 126.96.36.199 / Debian Wheezy 64-bit).
Another side effect is an immediate exit when
About | Welcome screen is diplayed. I believe, this code could be improved to correctly detect circumstances under which
MathematicaNavigator.nb was called.