Thanks again for the clarification, Vajradhara.
Time for a more thoughtful response to Thomas's answer from myself (The Fool is another alias I created for use on a shared computer today).
Especially as my original reply was simply sloppy and quite inaccurate.
The reason for the spread and dislocation (in some instances) is essentially because of political movements, which accompany the migration of people and ideas across continents.
Christianity in it's earliest period was a religious revolution. In contrast to the staunch Republican deities of Rome, Christianity was like a form of "spiritual communism" for the disenfranchised masses – the poor and the slaves, promised equality in the after-life, as well as providing ideological focus for richer philanthropic individuals (the humility teachings, such as the Beatitudes, being especially accessible to those who followed Stoic philosophy).
The principle engine for this "spiritual communism" was a two-pronged egalitarian ideal that was missing from state worship – that of Divinity caring and equally so.
Romans petitioned the classical gods not out of love, but of fear of loss and restitution, and to lament that broken things be fixed. But the gods are oft repeated in the classical literature across the Roman Empire as been cold and unfeeling.
Even in Ancient Greece, one did not petition the gods through a sense of love but of need, and only so – precisely because some other aspect of Divinity was affecting the petitioner in a way disliked. In simple terms, the polytheism was nothing more remarkable than animism with faces – the formless spirits of animistic belief having human form – likely built in the shape of the familial bodies of past warlords and chieftains (ie, an amalgamation of ancestor worship over with basic animist principles – though to what degree of each is a moot point).
Essential, through the entire Graeco-Roman pantheon, we see the forces of Nature personified, venerated, and feared – but, ultimately, often seen as unfeeling as the Natural World is wont to be. After all, by observation, Nature cares little for the individual, and inflicts disease and sorrow on the virtuous and criminal, the old and the young, in equal measure. This was the Nature that the Roman Gods represented - a natural order of the universe, different cycles with different faces, if you will - almost, even, a form of anthropomorphised physics.
So when Christianity came along and stated that there were not many gods, but a single God, who not only cared utterly for every living being, but that God had undergone an ultimate and torturous human sacrifice for the good of all humanity...well, then the audience can hardly have been anything but deeply affected.
We can see the proof of this both in the fast spread of Christianity throughout the Roman Empire (not as largely represented as some Christian authors would like us to believe – for example, Britain was never a significantly Christian province – it had the barest representation) – not least in the fact that it became very quickly dispersed.
Add to that the fact that, once officially sanctioned by Constantine and his dynasty, the workings of the Roman Emperor so-called "Julian the Apostate" could not turn the tide of Christian worship and reinstate the classical gods. Christianity had an appeal to the Romans that could not be overturned.
An especially eye-opening point about this era is that Rome was not destroyed by "pagans" – Alaric and his Goths that first sacked Rome were actually Arian Christians (following the teaching Arius: that Christ was human, not Divine).
To the point – the spread of the Christian Faith away from the Middle-East came with political separation from the Middle-East. Although it survived – still survives – in some small measure there, once Constantinople fell in 1453 then there was no direct protection for the Christians in the region, who remained essentially fragmented and disparate, despite that the position of Patriarch of Constantinople remained. Certainly this is the case in comparison to the previous protection that Byzantium held over the regions of the Near East, Asia, and North Africa, as a legacy from the Roman Empire and Julius Caesar himself. That was a particular papal concern when organising the First Crusafes at the end of the 11th century.
As to Islam: they were granted a gift in the fact that the Byzantines and Persians - the two superpowers, who ruled from Africa to europe to Mesopotamia - had essentially destroyed one another's military capabilities by the time of Mohammed's death.
Worn down and unable to respond to any further military action, Islam was able to take the early faithful across the Levant and Mesopotamia - taking Byzantine lands and even destroy the last vestiges of the Persian Empire itself.
Constantinople survived simply because the walls were impossible to impregnate by land assault - certainly by the methods of the time (the walls being breached only by Crusaders via the Venetian fleet (and aided by a deposed Byzantine Emperor) in 1204 - - - and then by the gunpowder of mighty bronze cannons actually cast on the battlefield in 1453).
As a particular point of note, Islam was not actually at first a proselytising religion – the Ummayid dynasty that ruled Islam for the first couple of centuries essentially worked as Judaism does now, where conversion is a far more complicated process than simply saying "I believe". It was the Abassyd dynasty, who came after and ruled until fragmentation of the Caliphate in the 13th century, who brought wholesale conversion to the civilian population. By then the major boundaries of Islam had already been drawn - - - and an oft repeated particular note is that the "people of the book" (ie, Jews and Christians) for the most part enjoyed special protection and privileges – and general respect - certainly in this period before the Crusades).
Of course, a major difference between Islam and Christianity is that it was the Christianised nations who embarked upon colonial exploration of the sea – and thus took Christianity across oceans, most particularly the North and South Americas. Islam itself was strictly a land-bound spread of faith, knowledge, and ideas, not least along the the trading routes that had crossed into Arabia and Mesopotamia.
So, the spread of Christianity and Islam – and Buddhism – has been principally through political movement – a consequence of the dynamic nature of humanity on our planet.
Intolerance was *never* a primary factor in the spread of Christianity and Islam – the militancy came later, in response to protection of expanded borders of faith from dissension within, and not least from one another without. But by then, both religions were very firmly established already.
