Q shows up on USS Voyager to introduce Kathryn Janeway to her godson, Q Junior, who now has the appearance of a human teenager.
Things start out bad with Junior around. He starts making all sorts of trouble for the Voyager crew, for example, turning Engineering into a nightclub, removing Neelix's voice, and starting a war between two peaceful races. He causes Seven of Nine's clothes to vanish, leaving her naked. When he sees that she isn't the least bit bothered and doesn't "scamper away" trying to cover up, he replaces them and goes on his way. He also puts Voyager against three Borg vessels, to see how "humans act under pressure," until his father appeared to clean up the mess (repairing the ship, removing the Borg vessels and drones, and restoring Neelix's voice).
Q explains to Janeway in her ready room that the Continuum hoped his son would stabilize everything. However, it was quite the opposite; Junior started war, tampered with primordial gene pools and tore holes in the fabric of space-time. The Continuum blamed Q for this, so he dumped his son on Voyager in hopes he'll learn something. Janeway suggests he spend some "father-son" time with Junior. But ten minutes later (one minute is one year in Q time), Q reappears seeking more advice. Junior was no better and had shifted the tectonic plates of a nearby planet and refused to apologize. Janeway says Q Junior must learn that there are consequences for his actions.
Disappointed by young Q's lack of progress, Q takes away his son's powers and he leaves once again. The Q Continuum has ruled that the boy will be turned into an amoeba unless he improves. After a rough start, young Q gains Icheb's trust and kidnaps him on the Delta Flyer on a tour of the galaxy. They run into a Chokuzan ship, which fires a neural weapon at the Delta Flyer leaving Icheb incapacitated. Young Q returns to Voyager and pleads with the Doctor to save Icheb. The Doctor is powerless without more knowledge of the Chokuzan weapon. When Q refuses to save Icheb, stating that if Q Junior's friend must die for him to learn his lesson, "so be it," Janeway and Q Junior return to the Chokuzan ship to plead for the information to save Icheb's life. Since Janeway was the adult responsible for the boys, she is the one to be punished. Q Junior argues against it, demanding he be the one punished, even if the penalty is death.
At this point Q finally reveals that the whole situation was just another test for his son, and there wasn't really a Chokuzan vessel after all. Janeway, frustrated at being toyed with, asks of Icheb's condition, to which Q replies that the doctor will find he has miraculously recovered. He then returns the trio to Voyager to stand judgment in front of the Continuum, where it is decided that although Q Junior hasn't shown enough improvement, he will not be turned into an amoeba. Instead, Q Junior will suffer the "second worst fate" of remaining forever in human form without his powers. The continuum then vanishes, followed by an upset Q.
Shortly after, while Janeway is talking with Q Junior, Q reappears with the news that if his son must leave the Continuum, then he will go as well. Knowing that Q is required to keep the Continuum relatively stable, they grant his appeal to restore his son's powers. Q Junior uses them to fill his "Aunt Kathy's" ready room with roses before disappearing. Janeway is clearly doubtful that the Continuum got on their knees and begged Q to stay as he said, so he admits there were a couple conditions such as eternal custody of his son. Finally, he gives Janeway information to take Voyager home sooner as a token of his appreciation. When she asks why he is only saving them a few years of travel instead of taking them all the way there, Q responds "What sort of an example would I be setting for my son if I did all the work for you?" and disappears.