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In the last episode of Dragon Ball Super there was a dialogue between Future Trunks and his father, Vegeta, regarding the use of the sword. According to Vegeta, there was no need to use it now, but Trunks said that the sword makes him feel safer and more comfortable. This dialogue has led to different theories and interpretations about the power of Trunks' sword, including the one that says that this sword is none other than the ZSword and another theory that says the sword was given to Trunks in the future by the Eastern Supreme Kai because he apparently trained him to fight against Dabura and Babidi.
These theories are not true and we are going to show you why. First, the Z Sword appears in the Majin Boo Saga when Gohan frees the weapon that was embedded in the Z Sword Plateau at the Sacred World of the Kais. The Old Kai, a deity from the fifteenth generation of Kai, was trapped inside, and it was later revealed that he was sealed there by Beerus, the God of Destruction. So if Trunks already had the sword before going to the past for the first time (Cell Saga), how could his sword be the Z-Sword? Some might say that Trunks' sword was destroyed during Cell Saga and that's why the sword he has now could be the Z-Sword. This is not true, in both the manga and the anime, Trunks' sword just got damaged on the edge but it could have been easily fixed.
Besides that obvious statement we know that the character who released itwas Gohan, whom, according to Trunks' timeline, the future, was dead by that time. Some might think, why couldn't Gohan release it before dying? Simply because he could have never done it since it's not possible to go to the Sacred World while being a simple mortal.
Let's remember that Gohan only went there when the Supreme Kai saw his skills to defeat Majin Boo. In the future, Majin Boo was never a real threat since Trunks prevented him from waking up (as it was said in the last episode).
On the other hand, its been said that while Trunks had the Time Machine he could have travelled and taken the sword somehow.
This makes no sense because the sword itself does not have any particular power despite being very resistant and heavy. Let's not forget that Gohan could released it thanks to his power and it took him a couple of hours of training to control it, but in the sword itself there weren't any powers. The real power isreached by the person who learns to control the sword after all the effort that was put in. Also, Trunks' sword from Dragon Ball Super and the ZSword are very different aesthetically. Akira Toriyama designed the Z-Sword with a type of jewel in the pommel while Trunks' sword doesn't have anything like that.