Challenge: Catholicism reigns supreme over its competitors

The Challenge: get a scenario where Catholicism (and a few smaller Churches in Communion with it) dominates all of Europe, the Middle East, and North Africa to this day. Islam, widespread Atheism, The Great Schism, and the Protestant Reformation are all either butterflied away, killed in the cradle, or undone by converting most of their followers back to Catholicism. Nothing, in the long long run, replaces the Church, and areas that were never Catholic either get Catholicicized or converted by a Church in Communion with the Catholic Church.

How can we make this happen?
 
I got one idea... Emperor Julian promoted heresy in the Roman Empire's Christian factions to strengthen his pagan faction. He sent back many churchmen who had been exiled in order to forment disagreement. Perhaps if he doesn't do this (probably by not being Emperor), the remaining church more quickly codifies their beliefs. This "Catholic" Church dominates all of the Empire. All the theological rebels that would make up the East, and the Arians in the West, are killed by an alternate Emperor who is madly devoted to the Nicene Creed. This prevents the split of Christianity into east and west, and the spread of Christianity much faster ITTL prevents Islam from ever forming. Complete solidarity and unity is found in the singular authority of the Bishop of Rome, Vicar of God on Earth.

That's my best shot.
 
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