The statements that do NOT reflect how the power of the Church in Western Europe grew by the year 1000 AD is "Collected tithes."
This is because the collection of tithes has been in existence since the days of Abraham, and it was found in Christendom in Europe around the 8th century.
Also, tithe collection has little effect on the emergence of the power of Churches in Western Europe by 1000 AD, as it adds little to them in terms of finances.
Hence, in this case, it is concluded that the correct answer is option A. "Collected tithes."
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