Flavor text quotes seem to imply that his intentions during the Phyrexian/Mirran war (and possibly his current intentions as well) were to turn Mirrodin into a form that he considers perfect, making him similar to his rival Jin-Gitaxias in goals, although very different in methods and most likely in the end result. Also like Jin-Gitaxias, he uses an alternative term to "Grand Evolution", the "Great Work", although whether he actually disagrees with established Phyrexian terminology is unknown.
After Phyrexia's conquest of Mirrodin, Urabrask allowed the Mirran survivors to take refuge in the furnace layer of the plane, which is controlled by him. This is due to the fact that he is aligned with the colour of emotion and freedom, granting him enough empathy not to (actively) destroy the Mirrans. This, coupled with sheer dislike of the other factions, led him to seal the Furnace Layer of the plane off from other Phyrexian factions. For the most part, they don't seem to care either, with the exception of the blue-aligned Progress Engine, which is paranoid about this.
Inevitably, Elesh Norn laid waste to his domain. It's unknown if Urabrask still lives, though the Mirran Resistance fled to the moutain shelters, out of reach of Elesh Norn.
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