I'm using Ubuntu 13.04 with MATE desktop, and I would like to replace Plymouth with good old Xsplash. But I have no idea how to do that...
You don't. Not only is Plymouth an integral part of Ubuntu, but xsplash was removed from the archive.
Plymouth is more than simply eye candy to look at during boot. It multiplexes console access among multiple startup tasks that may need user attention. This functionality is required to use