Has the Global South been influential in the old churches they derive their existence from?

It is said that there are more Anglicans attending Sunday morning services in Nigeria alone than in all the United Kingdom. Recently the archbishop of Lagos has effectively excommunicated the archbishop of Canterbury for gross heresy; other communions such as Baptists, Methodists and even Roman Catholics have been seeing similar patterns in different stages. Philip Jenkins thinks this is but the beginning of a new cycle according to a pattern that repeats itself again and again since the early days of the church. The question is, while we have influential examples in Global South bishops and preachers, how influential are them in the Old World and North America?