This is what Wikipedia offers for the Late Pretenders:
After Alfonso Carlos' death, dynastic seniority — after the Salic law — fell upon Alfonso XIII, former constitutional King of Spain and then in exile at Rome, therefore, at least in theory, ending the family split. But according to the theory of legitimacy in exercise, many Carlists thought that Alfonso XIII and his heir Juan de Borbón were radically disqualified to head the "Cause". They cited the doubts over Alfonso XII's paternity to dismiss him as illegitimate and his descendants as thus ineligible for the throne.
Alfonso Carlos had named in 1936 Prince Francis Xavier of Borbón-Parma as regent, as he was the nearest Bourbon who shared the Carlist ideals. During the Second World War, Prince Xavier returned to the Belgian army, where he had served during World War I. He was demobilized and joined the French maquis. He was taken prisoner by the Nazis and sent to Natzweiler and Dachau, where the American troops liberated him in 1945.
In 1952 he laid openly his claims to the Throne, which he ceded in 1975 to his eldest son Carlos-Hugo, married to Princess Irene of the Netherlands. After the definitive break with Franco (1965–1967), under the latter's direction, his group switched to a leftist Titoist, autogestionary socialist movement. His brother, Sixto of Borbon-Parma, has headed a far right split.
In 1980, Carlos-Hugo left the political arena, but did not abdicate his rights.
In 1958, a sizable group of Carlists, recognized Juan de Borbón as his Head.
From 1943 to 1953, the Archduke Carlos-Pio of Habsburg-Lorraine-Tuscany, claimed also the Head of the House.
Beside them, there were other factions, which recognized neither of the above. Some were tightly integrated in the Movimiento Nacional, some were not.
Most of this events happened under Franco's regime, which skillfully played one group against the other, and all of them against Don Juan.