BEIRUT, Lebanon — THE letter bore the corporate tone of a C.E.O. resolving a turf dispute between two middle managers. In formal prose and numbered lists, Ayman al-Zawahri, the leader of Al Qaeda, directed one of the group’s affiliates in Syria to withdraw to Iraq and leave operations in Syria to someone else.

The response was unequivocal. Abu Bakr al-Baghdadi, the leader of the Islamic State in Iraq and Syria, or ISIS, declared that his fighters would remain in Syria “as long as we have a vein that pumps and an eye that blinks.”

It was the first time in the history of the world’s most notorious terrorist organization that one of the affiliates had publicly broken with the international leadership, and the news sent shock waves through the online forums where jihadists meet. In no uncertain terms, ISIS had gone rogue.

That split, in June, was a watershed moment in the vast decentralization of Al Qaeda and its ideology since 9/11. As the power of the central leadership created by Osama bin Laden has declined, the vanguard of violent jihad has been taken up by an array of groups in a dozen countries across Africa and the Middle East, attacking Western interests in Algeria and Libya, training bombers in Yemen, seizing territory in Syria and Iraq, and gunning down shoppers in Kenya.