Ah right, I saw this question earlier but was too busy to answer.

The body remains where it is or was if it was completely destroyed. This is the immortals most fragile point as anybody can do anything with the bodies afterward; which goes to my lore where immortals have been captured but never held, usually because when they wake up, they usually escape with the use of magic or another group of immortals comes to get them out.

Immortals work together to try and prevent this, so if one dies, the other(s) can take the body to a safe place so they can resurrect. If a body is completely destroyed, it's advisable to just keep an eye on the area and be ready for when the immortal resurrects. Body parts come back in an instant flash of light, so a full body being resurrected is just an incredibly bright flash and boom, human. It should be noted that clothes don't regenerate with the immortal, so the others on recovery duty should pack a change of clothes for them when they return. :P

This information will be added to the Immortals codex entry after I have gotten the rest of the codex established so people can begin working on their characters in full detail.