So I've heard that when the Normans took over England, they managed to make it the most centralized state in medieval Europe at the time. How and why did they do this? Was it simply because of the issue of a conquering population needing to rule over a separate subjugated ethnic group, or were there other reasons?
I'm afraid I've never heard this argument before. Rather, what is generally agreed upon is that Anglo-Saxon England was an unusually centralized state, and the Normans inherited and wisely continued that state of affairs.
Unlike France and to an extent Germany, royal power never collapsed in England. While there was a landed nobility, they were not as powerful as their continental counterparts, and the Norman redistribution of land made them even less so. Great lords did not possess entire regions of England, as in France; rather, they held land scattered throughout the country. The kingdom was divided up into shires, and each shire was administered by a royal official, the sheriff, who was responsible for raising troops, maintaining order, and collecting moneys due to the crown.