: : : The corporeal form is an irrelevance, a Maiar is spirit in essence, and the corporeal form it takes is not of the same intrinsic/essential quality as a Man or Dwarf or Hobbit (Elves are a little more complicated)
: : : The point is, when the ring was cut from the hand, Saurons spirit which inhabited it (that part of his spirit anyway) was torn from him, and his essence fled in pain and fear. Whatever if anything was left behind is irrelevant - it was not Sauron anymore in any way shape or form.

: : You are correct that to the overall scheme of ME that Saruon's corporeal form is irrelevant, but so too are dwarf wings and ent ears. ;)

: : It does, however, remain a question, and one worthy of discussion as Sauron seems to be impacted by the loss of his corporeal body, to the point that he did not, or could not, reform one of his fingers. Whether or not the body left behind by Sauron was "not Sauron anymore in any way shape or form" was never asked. What began this thread was what became of the body?

: : -RR

: What happened to the body? There would be no body. Sauron's body(form), corporeal or otherwise, was maintained by his spirit. Once his spirit fled the form, the form would cease to exist. It would either crumble,like Saruman's, or simply vanish.

: While the loss of his body did weaken Sauron's spirit, the loss of his spirit within the Ring weakened him even more. Following the destruction of his body during the downfall of Numenor, he possessed the Ring and took a new form far more quickly than he did following the loss of the Ring.

: As I say, in my reply above, I believe it was his spirit trapped in the Ring that prevented him from taking a complete,in this case ten fingered, form.
: ~Aelmer

The corporeal form of Sauron is not an irrelevance. The mere threat of serious damage to his fana in the First Age (a dog had him by the throat) was sufficient to send him scurrying into hiding. This is when he was not particularily wedded to a single corporeal form. The threat to his abilities and effective existence of physical damage was far greater after the Akkalabeth when his form became fixed.

Isildur cut the finger and Ring off Sauron when he had been severly wounded by Gil-galad and Elendil and could not put up effective resistance. Sauron had been rendered incapable by physical actions and physical weapons (though these probably had spiritual dimensions also). The reason Sauron could not regenerate his finger was that it had been cut off by one of the shards of Narsil not that the Ring was lost. If Sauron had merely taken off the Ring would his finger have dissappeared?

I imagine that either Sauron's spirit was so wedded to his physical form that any mutilation of one affected the other; or that Narsil had a particular quality which deranged Sauron's spirit even as it mutilated his body.

The loss of the Ring did have grave effects, as you say, on Sauron's abilities to regenerate quickly, but not I think on his ability to regenerate his digit.

We have every reason to beleive that the form Sauron took following the Akkalabeth was different to a "normal" Ainu fana, therefore it would be distinct from that of Saruman or Gandalf (when Grey) and even these were different from normal fanas (they aged in appearence). It therefore is not safe to extrapolate the fate of Sauron's inert body from that of Saruman or that of any other Maia.