The demons' counterpart to Yggdrasil is the supercomputer Nidheg which fullfills roughly the same control functions. To keep the battle between gods and demons from escalating, demons are not allowed to hack into this heavenly control system, with goddesses probably operating under similar regulations. As an additional safeguard, the doublet system links one goddesses' life to one demon's, thus avoiding the loss of life during their fights.
During the Lord of Terror events, it became clear that Yggdrasil controls the very foundation of our world, the so called universal superstring which comprises among other things every atom of the universe. After this superstring had been destroyed, the supercomputer could reconstruct - and apparently also emulate - it, saving our universe from ceasing to exist.
Mythological Background EditIn Norse Mythology, Yggdrasil is the World Ash, a giant ash tree which connects all nine worlds of this mythology - among them Midgard ("Middle-earth"), realm of the humans, and Asgard, realm of the gods. Next to one of its three roots, the Norns - on which Belldandy, Urd and Skuld are loosely based (at least their names are) - live and water this tree from the Well of Urd, keeping it evergreen and vital.
When this most holy of all trees in Norse Mythology withers, Ragnarok - the end of the world - begins with the Wolf of Fenrir breaking free and the Midgard Serpent rising from the oceans. With the birth of these evil creatures and the arrival of the Giants, everyone assembles for the final battle, destroying most of the life in the universe.