After Infinite Crisis, Earth 13 it was assumed as the universe where all characters originally from DC universe were being published by Vertigo Comics. That universe includes: Swamp Thing, John Constantine, Shade the changing man, Doom Patrol, the characters of Book of Magic, Animal Man, Sandman (both, Neil Gaiman's and Matt Wagner's). Mostly, the most magic, dark, supernatural users. As most of events in these books were more self-contained and followed their own continuity, with writers working with a bigger creative freedom and unrestrictive continuity. The contradictions left a world different from the main DCU and the explanation was accepted.
Earth-13 was created by Keith Champagne and Scott McDaniel
Vertigoverse / Earth-13
During Countdown, Earth-13 was presented with the inclusion of Brigadier Atom (a Captain Atom analog) and Eve of Shadows (Nightshade analog). They saw the partial destruction of Earth-13. However, these events are apochrypha to the Earth-13 accepted definition.
During 2011, the Vertigo characters were returned to the main DC continuity. This movement, motivated by editorial directives and changes in the administration of Vertigo comics. The change was illustrated in Flashpoint #5, where the Vertigo line characters were defined as belonging to a different timeline. At least, under this light, it can be said than this Earth-13(vertigo earth) it fused to the main universe, reaching its end.
The New 52 / Earth-13
Defined as a world where magic and technology coexist, the Earth-13 present in Multiversity keeps the Vertigo atmosphere from its predecessor, but with bigger differences. The official description from Earth-13 reals than is a world in a orbit in a perpetual state of magical twilight. A world of years of 13 months and days of 13 hours. Its strange combination of heroes and history adds to its uniqueness.
The characters of these world includes amalgams of magical characters, not only from Vertigo, but also from the main DCU: The main hero of this world is Superdemon, a demon with with powers and abilities far beyond those of immortal creatures, who is a mix of Superman and Etrigan; Joined by Hellblazer, (John Constantine full-filling the role of Batman). Fate, from the Weirdoverse is also now a native from this reality. Other characters as Annataz (An inversed Zatanna), Witchboy, Swamp-Man, Ragman, Deadman and Enchantress are darker versions from their main Prime Earth analogs. This strange faction has banded together as the League of Shadows
But make no mistake, this is not a place one simply pulls a rabbit from a hat and calls it magic. This is a world of the occult—where the supernatural is real. Where the mystical sorcery is so thick, you breathe it in the air, allowing your senses to tingle with the aroma of witchcraft. The veil between the realm of spirits and corporal are thinnest on Earth-13. No, your eyes haven’t deceived you—that’s exactly what you thought you saw. On Earth-13, the darkness is your light.