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An immortal unit will respawn in it's home province after a number of turns, unless it was taken by an opponent. The time varies but is indicated in the ability description. A unit which reforms its body successfully may cure some of its afflictions in the process. In effect, this means no matter how often it dies, it can be used again and again and is one of the reasons Liches and Vampire Lord's are considered powerful.
There are however a number of means to prevent immortality from triggering - any form of soul destruction, whether through the spell Soul Slay or other effects like Devour Soul or Consume Soul. Certain items such as the Ethereal Crossbow also provide this effect. Additionally, if unit's origin province is not under control of its owner when an immortal attempts to reform their body, they will be unable to come back and will function as if they had died a normal death.
Immortals may also be mitigated by using spells such as Charm or Enslave Mind which take ownership of the immortal rather than killing it.
A number of variations exist of standard immortality, which impose additional conditions.