Mantling is a process in the Elder Scrolls universe by which one entity becomes another entity by impersonating it. In most known or speculated instances of this process, the entity being mantled is a deity, while the person mantling is a mortal.
Merely impersonating someone publicly is not enough to mantle them. To mantle someone, you must become so like them that there ceases to be a functional difference between the two entities; it seems that at this point the universe itself ceases to distinguish between the two, and they become one entity.
It seems that while mantling does involve, to some extent, assuming some other entity's identity, this does not appear to necessarily involve giving up the mantler's own identity, at least in full.
The concept of mantling is unique in that it has few, if any references to it in any major Elder Scrolls game, despite having been confirmed to exist in the universe by several developers, particularly on The Imperial Library. There are some books which reference events that could be mantling, however it has never been referred to specifically by its name.
Tiber Septim and LorkhanEdit
Mantling may have been what caused Tiber Septim to become the deity Talos upon his death; he spent much of his life campaigning around Tamriel with the Numidium, which was originally constructed to draw power from the Heart of Lorkhan. While the Numidium in Tiber Septim's possession was powered by the Mantella, not the Heart, it is possible that so much time spent around and controlling the Numidium's power was enough for him to effectively mantle Lorkhan, and take his place among the Nine.
This example also supports the idea that mantling may be influenced by voids of power or identity in the universe; Lorkhan, while known, was not an active deity, and this absence of direction in his power might have made him more prone to being mantled. Understood another way, it may have been easier for Tiber Septim to mantle Lorkhan (either intentionally or not) because the universe itself wanted a ninth deity to direct Lorkhan's power. Though this would raise many questions about the nature of the power from the Heart of Lorkhan, and whether it affected or was affected by Tiber Septim becoming a deity.
Tribunal Temple and the Daedric PrincesEdit
After the War of the First Council Sotha Sil acquired an understanding of how the tools of Kagrenac and the Heart of Lorkhan work, and thus how to use them to turn the Tribunal into living gods. The Tribunal then went through the process to steal its divine essence for themselves. Azura then appeared before them and cursed them for their sacrilege, and then subsequently the entire Chimer race after Sotha Sil angered her by saying that they didn't need the Daedra anymore, as the Tribunal were the new gods of the Chimer people. It was then that the Tribunal of Vivec, Almalexia and Sotha Sil became known as the "False Tribunal" while Boethiah, Azura and Mephala became the "True Tribunal". Each member of the "False Tribunal" mantled one of the "True Tribunal".
Vivec's "Anticipation" is the Daedric Prince Mephala. He also shares some of the darker sides that characterize Mephala, such as secretive murder. Boethiah is Almalexia's anticipation, during the events of The Elder Scrolls III: Tribunal she betrays Sotha Sil, further showing why she mantled Boethiah, Daedric Prince of deceit, conspiracy, treachery. Sotha Sil's Anticipation is Azura.
Champion of Cyrodiil and SheogorathEdit
The Champion of Cyrodiil was given the mantle of Sheogorath at the end of the Greymarch. The exact nature of this mantling is difficult to understand in full. Rather than acting like Sheogorath until the universe effectively combined the two entities, Jyggalag surrendered the Mantle, or role, of Sheogorath to the mortal Champion of Cyrodiil.
Over time, the Champion assumed the role of Sheogorath. However as evidenced during the events of Skyrim, Sheogorath underwent a personality shift. Rather than his Daedric Quest requiring something along the lines of making it rain flaming dogs, it required curing a long-dead Emperor. This could be a result of both entities, The Champion and Sheogorath, mutually mantling each-other. Sheogorath assuming a more heroic stance, causing him to actually cure madness in a long-dead emperor. The mortal Champion of Cyrodiil on the other hand became more neurotic, leading to his mimicking Sheogorath's eternal leaping across the entire spectrum of madness.