What is it called when the Church has 3 popes?

Answer 1

While there were never actually three Roman "Catholic" popes at one time, there were three who claimed to be at one time. The actual pope, recognized by Rome, is/was the "Pope". The others are called the "anti-popes", aka, illegitimate popes.

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Catholic AnswerIn the 14th century, when the Church had three different claimants to the papal throne, it was called the Great Schism, not to be confused with the Schism of the East three centuries earlier. It is also referred to as the Avignon Papacy as the true pope was not in Rome, at that time, but in Avignon, France.

from

A Catholic Dictionary, edited by Donald Attwater, Second edition, revised 1957

The Great Schism, otherwise know as the Schism of the West was not strictly a schism at all but a conflict between the two parties within the Church each claiming to support the true pope. Three months after the election of Urban VI, in 1378, the fifteen electing cardinals declared that they had appointed him only as a temporary vicar and that in any case the election was invalid as made under fear of violence from the Roman mob. Urban retorted by naming twenty-eight new cardinals, and the others at once proceeded to elect Cardinal Robert of Geneva as Pope Clement VII, who went to reside at Avignon. The quarrel was in its origin not a theological or religious one, but was caused by the ambition and jealousy of French influence, which was supported to some extent for political reasons by Spain, Naples, Provence, and Scotland; England, Germany, Scandinavia, Wales, Ireland, Portugal, Flanders and Hungary stood by what they believe to be the true pope at Rome. The Church was torn from top to bottom by the schism, both sides in good faith (it was impossible to know to whom allegiance was due), which lasted with its two lines of popes (and at one time three) till the election of Martin V in 1417. It is now regarded as practically certain that the Urbanist popes were the true ones and their names are included in semi-official lists; moreover, the ordinal numbers of the Clementine claimants (who, however, are not called anti-popes,) were adopted by subsequent popes of the same name.