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Tibi Gon paused in his tracks when he heard the slight whimper coming from the alley. He followed the sound to its source, one of the city's numerous jinn (what the locals called street children and orphans). The child was small and starved, and couldn't have been more than three years old.
Tibi paused, he couldn't leave the child to starve on the streets, and the planet didn't have any children's homes or orphanages. He reached a decision, he would bring the child with him. His mission was finished and he was on his way back to Coruscant. On Coruscant he would find someone to care for the child.
He knelt down to pick up the small child, and was suddenly thrown backwards. He knew exactly who would be caring for the child in the future. This time Master Yoda wouldn't be able to find fault in his picking up of yet another stray.
Tibi focused, and used the force to create an aura of calmness and harmlessness. The child cautiously crawled forward. Tibi gently picked it up and carried it from the alley. Upon reaching his transport home, he promptly carried the small child into the tiny washroom at the back of the ship and removed its clothes. The child was a rather dirty human boy of approximately two and a half years of age. Tibi cleaned the child and wrapped him in his spare cloak until the rags the child had been wearing were clean.
Tibi then carried the child into another section of the ship, where he prepared a meal for the boy. After eating his fill, the child grew tired and fell asleep. As Tibi carried the child to a spare bunk, he began to think about what to call the child.
"Part of your name will be Jinn, so you don't forget where you came from. As for the rest of your name, I think I will call you Qui Gon, after my father, he was an honourable man who fought his way from the gutters to a top position in a profitable company. Where you come from doesn't always determine your fate child." Tibi whispered as he tucked the sleeping child into his bunk.
A week later, Jedi Master Tibi Gon and a small skittish child named Qui Gon Jinn arrived on Coruscant.
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Author's Note: In the Phantom Menace, it was noted that Qui Gon had a habit of picking up strays. I kinda wondered if Qui Gon hadn't started off as a stray himself, that could be one explaination of his behavior.