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You could make the welcome page available only to anonymous users, and then when people log in, they cease to be anonymous and the welcome message should disappear.
If your message is simple enough, you might want to just make a custom block and put it in the centre column, and give the anon users permission for that block, but don't let anyone else see it.
I believe you need to install the TinyD version of Tinycontent in order to have group access permissions for the stuff in Tinycontent, but I could be wrong about that.
Hope this helps,
--Julian