Throughout the Doctor's adventures, he accumulated much knowledge and experience that was codified in his biodata. During the War, much of that information, such as the biodata codes of assorted Time Lord presidents, was lost. Thus, when the Doctor died, his body became very valuable to many Wartime powers including the Time Lords, Faction Paradox, UNISYC, the Daleks, the Krotons, the Celestis, and the Enemy.
Despite being dead, the Relic was unusually powerful. Most psychics retained some power even after death, depending on their powers while alive; the Doctor's psychic potential was so significant that the Relic was still generating a psychic "call", particularly attuned to nearby humans, long after the Doctor's death.
The Relic was contained in a metal box with the Greek letters "Theta" and "Sigma" on it.
Two days between the first battle of the War, one of the more interventionist and optimistic members of the Great Houses visited Dronid, claiming he had an old connection to one of the enemy's agents there. However, his diplomatic attempt apparently failed; he was thought to have died as the battle started. (PROSE: The Book of the War) However, Qixotl was involved in the true story of the Doctor's death, which was much more complicated; the Relic had been intentionally planted in a bunker under the ruins of the city centre of Smithmanstown.
There, it was found by the Corporation. Celestis agents worked with Little Brother Kolman to steal it for Faction Paradox, but Cousin Sanjira didn't recognise its importance and instructed Little Sister Justine to dematerialise it. From there, it crashed onto Earth and was put in the Toy Store, which was pillaged when the Daleks invaded. By 2169, the Black Man had it in his store in London, though he sold it to Qixotl shortly before Homunculette came looking for it.
Qixotl set up an auction for the Relic on Earth in the late 21st century, creating the Unthinkable City to hold it. He invited only a select group of people interested in the Doctor's body for an actual purpose, rather than risking inviting those who just wanted to mutilate it for revenge against him. The auction did not go to plan, due to such factors as the Krotons taking the place of the Daleks and the inherent danger of the various powers bidding for the Relic. The Eighth Doctor arrived after hearing news of the auction and soon determined what the Relic actually was, even if he avoided learning any specific details about where or how he would die in the future. During the subsequent crisis, at one point the Doctor managed to link with the Relic's psychic energy to expel a Faction Paradox agent that had possessed one of the human delegates. Having tricked the various groups at the auction into thinking that the Relic was a temporal paradox by convincing the Celestis that they had "marked" him as their agent in this body rather than immediately prior to his death (in reality they had marked the conceptual entity known as the Shift that had been trapped in the Doctor's mind), the Doctor was able to leave with the Relic. He took it to the planet Quiescia and destroyed it. (PROSE: Alien Bodies)