How do you think the division of the christian church into clergy and laity them spread their beliefs?

He Roman Empire basically split into two parts - the Western, and Eastern halves. The East was somewhat protected by geography from invaders, but, the West was not so lucky. So, the Roman civil structure broke down. 

The Church ended up filling the void, as they had trained staff, and communications lines to Rome, where the Patriarch of the West was (now called the Pope). The town hall - the Basilica, became church property, and so on. This did not happen in the East. Civil authority remained, and the Church stuck to church things.