What makes an anti-pope an anti-pope, and who has the authority to declare one?

The only one who can determine that a pope is an anti-pope is another pope, because he alone has the authority, and that is how the system survives. We should be thankful that no cardinal, group of cardinals, or council has the power to depose a pope, no matter how respected, because otherwise, over Catholic history, popes would have been deposed constantly. The law is clear that the pope cannot be judged. So even if a man is an anti-pope, we have to put up with him, and the determination comes only afterward, from a later pope, who can gather the evidence, make the judgment, and then decide case by case whether to uphold or negate the previous pope's decisions. We have had about forty-four such instances. This is exactly what has protected the Church for two thousand years.