OTL, Raymond IV, Count of Toulouse, was one of the most important leaders of the Crusade and a peculiar one.
He is the only one not to have sworn fealty to Byzantine Emperor Alexius I, but he offered him Friendship. Later, he would ally with Alexius I against a common ennemy, Bohemond of Tarente, prince of Antioch.
Raymond was also offered the crown of Jerusalem, but he refused to rule the city where Christ himself had suffered and the crown went to Godfrey of Bouillon. In his last years, Raymond worked to built himself a county in the Holy Land, and his descendants would effectively rule the County of Tripoli.
However, what if Raymond had decided to accept the crown of Jerusalem?
What would happen to the county of Toulouse?
What would be the relationship between Byzantium and the Crusaders in this case?
And lastly, how would Raymond's leadership be seen by the Crusaders?