Version:           3.1.0 (using KDE 4.1.0)
Installed from:    SuSE RPMs
OS:                Linux

When i quit kate from ctrl+q, file\exit or exit button of the toolbar, kate quit normally.
When i close kate using the button close of the window, the kate's window close, but the process figure to be still active, not zombie and it still occupies memory.
When i start another kate, the previous process don't close yet, so if i close also the last from the window manager, the window closes but i will have two kate still in memory.
A "kill" with SIGQUIT, SIGHUP, SIGTERM to kate closes the processes remained in memory.
I tried with and without plugins, but it shows the same behaviour.