Jedi transport 634, an Eta-class shuttle, served as the vessel for Obi-Wan Kenobi, Anakin Skywalker, and Ahsoka Tano during their venture into Wild Space, which ultimately resulted in locating Mortis. The Force-sensitive being called the Son had the desire to utilize the transport to flee Mortis, so Ahsoka intentionally damaged it, preventing his release into the galaxy. Following the passing of the Father and the Son, the Jedi regained consciousness within the transport, which was suspended in space.
As an Eta-class shuttle, the Jedi transport 634 measured 14.2 meters in length, featuring a dorsal fin and a pair of wings that retracted upon landing. It required two pilots for operation and possessed a hyperdrive system. Furthermore, the transport was equipped with two Undicur-class jumpspeeders.
In 20 BBY, amidst the Clone Wars, Republic Military personnel intercepted an ancient Jedi SOS emanating from the depths of the Chrelythiumn system within Wild Space. Consequently, the Jedi High Council sent Jedi Master Obi-Wan Kenobi, Jedi Knight Anakin Skywalker, and Padawan Ahsoka Tano to investigate. The trio journeyed to the isolated star system aboard transport 634, with intentions of meeting up with a Venator-class Star Destroyer. However, upon the transport's arrival at its destination, Skywalker contacted Clone Captain Rex aboard the Star Destroyer, as he believed the capital ship had not yet arrived. Rex responded that he was present within the system, awaiting their arrival: the two starships, despite their proximity, were unable to perceive or detect one another, either visually or via scanners. Abruptly, the communications signal ceased, as the transport experienced a sudden shutdown, followed by an equally abrupt reactivation. Subsequently, the three Jedi observed a massive octahedral monolith in the space before them. The monolith commenced opening, emitting a blinding white light as transport 634 was drawn inside, causing the Jedi to lose consciousness.

Kenobi, Skywalker, and Tano awoke inside the transport to discover it had landed in the center of a meadow on what, according to the ship's instruments, appeared to be some form of organic matter. Upon disembarking, they encountered an alien environment characterized by floating rocks and were soon greeted by a mysterious woman identifying herself as Daughter, who inquired of Skywalker whether he was "the one." She directed the group to accompany her, but after Kenobi and Tano became separated from Skywalker and the Daughter due to a landslide, the two decided to return to the ship. However, upon their return to the meadow, Kenobi and Tano discovered that the transport had disappeared. Because of the perilous nighttime storms of their location, Mortis, the pair were compelled to spend the night within a nearby cave before being abducted in the morning by the Daughter and her brother, the Son, at their father's behest, as he wished to assess Skywalker to determine if he was indeed the Chosen One of prophecy. Following Skywalker's successful completion of the Father's trial, he declined an offer to remain, and the three subsequently boarded their recovered ship to depart.
However, as the Jedi were attempting to leave, Skywalker succumbed to sleep in the hold and experienced a nightmarish vision of the Son, awakening to find that the Son had boarded the transport and was observing him as he abducted Tano. Skywalker then assumed control of the ship from Kenobi and pursued the Son through the fog and rock formations, ultimately crashing the transport after nearly colliding with the Son's tower. Despite Kenobi's suggestion to seek assistance from the Father, Skywalker embarked on a solitary mission to rescue Tano. Kenobi, remaining at the crash site, pondered how to reach the Father and promptly found himself beneath the Father's monastery. Kenobi arrived just in time to witness the Father being attacked by the Son, resulting in injuries too severe for him to aid the Jedi. Nonetheless, the Daughter was convinced to lead Kenobi to the Altar of Mortis, where he was presented with a dagger capable of killing the Son. In a confrontation at the Son's tower, Skywalker and Kenobi battled Tano, who had been forcibly converted to the dark side of the Force by the Son, before the Son managed to seize the dagger, inadvertently killing his sister when she leaped into the weapon's trajectory to protect her father. Subsequently, the Daughter bestowed her remaining life force to revive Tano, and the Jedi departed the scene.

Upon returning to the damaged transport, Tano commenced repairs while Skywalker, concerned about the Son, resolved to seek out the Father. Tano informed Kenobi of a series of issues with the ship, including fractured shilo pins and a compromised power converter, as well as advising that the engines be ignited twice to expel debris and that the backup vents required charging. Following Skywalker's departure, Kenobi, growing anxious, decided to embark on a search, requesting Tano to disable the firing drives, a task she was hesitant to undertake. When the Father revealed that Skywalker had ventured to the Well of the Dark Side in pursuit of the Son, Kenobi departed, instructing Tano to remain with the ship.
At the Well, Skywalker was presented with a vision of his future as the Sith Lord Darth Vader, an experience so appalling that he ultimately aligned himself with the Son, much to Kenobi's dismay and bewilderment upon his arrival. Skywalker commandeered Kenobi's speeder bike and marooned him at the Well, returning to the transport. However, Kenobi contacted Tano prior to Skywalker's arrival, cautioning her about the events that had transpired and instructing her to sabotage the ship to prevent Skywalker and the Son from departing, a request that irritated Tano as she had just completed her repairs. Upon Skywalker's arrival, Tano evaded him by clinging to the ceiling before escaping on the jumpspeeder he had arrived on. Skywalker was enraged to discover the sabotage. He attempted to transmit a distress signal, suspecting that no one could receive it. This did not concern the Son, who asserted that he would soon be able to attract any ship to Mortis, before departing to secure the Dagger. Skywalker was then approached by the Father, who erased his memory of the future the Son had revealed to him, restoring him to the light side. Meanwhile, Tano retrieved Kenobi from the Well, displaying the crucial component she had removed from the transport.
Skywalker was escorted to the monastery by the Father, and upon the arrival of Kenobi and Tano, the group collaborated to eliminate the Son once and for all. The Father eventually employed the dagger to end his own life, rendering the Son vulnerable to Skywalker's lightsaber strike. The demise of the final two Force wielders caused the monastery to collapse, unleashing a blinding light. When the Jedi reawakened, they found themselves once again aboard transport 634 in space, where they were contacted by Rex. They learned from the Captain that, from his perspective, their transport had only briefly disappeared from the Star Destroyer's sensors. After Skywalker insisted that they had been absent for a longer duration, a claim that Rex found perplexing, the Jedi Knight piloted the transport to rendezvous with the Star Destroyer.