The Continuum vs. Q was a legal case in 2378, in which the Q Continuum judged whether Q Junior had sufficiently improved his character to be reinstated as a Q, or would be transformed into an Oprelian amoeba to live out the rest of eternity.
According to an agreement between Q and the Continuum, his son had been given a week aboard the Federation starship USS Voyager as a Human to change his ways and become an "upstanding citizen of the cosmos". During this period, Q engineered a situation in which Icheb was critically injured by an apparent Chokuzan warship while on a joyride with Q Junior, forcing the younger Q to admit his culpability in order to obtain medical treatment.
Q hoped that the Chokuzan incident would sway the Continuum in his son's favor, but when the court convened aboard Voyager, the Continuum judged against him due to the fact that Q Junior's actions had placed Icheb in danger in the first place. However, in light of Q Junior's progress, the judges decided not to sentence him to existing as an amoeba but the "next worst fate": a Human. Afterward, Q was able to bargain with the Continuum to return his son's powers, in exchange for eternal custody of him. (VOY: "Q2")