Much of the conversion happened through dhimmitude. When the Arab muslims swept across North Africa they came with the sword and forced conversion on many, but most (mostly christians at the time) were converted by economic pressure and intimidation. For many, "Christianity" was about culture rather than personal faith, and when it became more convenient to recite the Shahada (There is no Allah but Allah, and Mxxxxxxx is His prophet), and dispense with the extra taxes and harrassments meted out to "christians,", people did it. For all the violence in the Muslim countries, it is really the passive acceptance of Islam by the majority that makes the violence successful.
Dhimmitude is quite remarkably similar to the conditions imposed on Ireland via the penal laws intended to encourage Irish Catholics to become Protestants. Didn’t work as well in Ireland as in Islam.
There is no Allah but Satan, and Muhammad is his pedophile.