I covered some aspects of this question two weeks ago on the short answers thread here

But I'll expand it further now.

You're asking two separate questions; How did the frankish dominated empire become a German dominant one? And how did the empire decentralize?

So starting from the beginning with Charlemagne, king of the Franks. He's often associated with the French as French as a name comes from the Franks but he did not speak that Romance language, his Frankish was still west germanic and more or less intelligible with the other germanic dialects around the Rhine. This is to point out that the German component of the empire was always there.

Charlemagne was crowned emperor of the Romans in 800 due to the usurpation of Irene in Constantinople and because of Charlemagne's protection over the Pope & Rome.

His Empire passed whole to his last surviving son, Louis the pious. This is important as the Franks still followed germanic law so inheritance split equally to all sons. Which is what happened with Louis' death and what ultimately really confuses what should be pretty straight forward.

Louis's sons rebelled against Louis near the end of his life as he attempted to pass the imperial title to Charles the bald, his youngest son and from a second marriage. Louis' 3 eldest sons; lothair, Pepin, and Louis (the German) controlled sections of the empire and fought their father. Pepin dying before his brother.

After louis the pious death, the Empire split with Lothair gaining the middle section including Italy and the Imperial title as Italy was the most prestigious part with the city of Rome.

Louis the German got East Frankia and Charles the Bald west frankia. All 3 sections were supposed to be equals and United under the emperor, what really happened is that the line of Charlemagne had 3 rightful lines of heirs and they all wanted the imperial crown. Italy May be the most prestigious, but it wasn't the strongest. What began was decades of civil wars and the imperial title being passed around like hotcakes as the strongest line either threatens the pope directly into crowning him, or the Pope actively gives it to someone else as a power play.

This is important as these wars create the 3 separate spheres of power which I'll call France, Germany, and Italy out of simplicity but that is an anachronism.

The empire would reunite for the final time under Charles the Fat, son of Louis the German in 884 by the inheritance of his brothers. Charles wasn't a good emperor and when before there were too many legitimate Carolingian heirs, now there wasn't enough as Charles had no sons and he would be overthrown by his nephew Arnulf, a bastard of Charles brother in late 887.

Arnulf would become King of Germany in 887 but France and Italy chose new kings through election. Odo, count of Paris became king of France and Guy of spoletto became king of Italy & emperor with support of the pope.

So Arnulf is the last of the Carolingians but through an illegitimate line. Arnulf would expand Germany and secure his rule there while Italy fell into civil war. And the pope requested Arnulf's aid as the most powerful monarch.

Arnulf invaded Italy in 894 and was crowned king of Italy but had to leave to clean up trouble north of the alps. In 896 he returned and was crowned emperor but there was still trouble in Italy. And the emperor only had control when in Italy directly. Arnulf would die in 899 and pass the German crown to his minor son, Louis the child.

As we can see, the imperial center of power has already shifted to Germany but the imperial title is still connected to the kingdom of Italy which is in a perpetual state of civil war between different nobles and popes. Louis the blind becomes Italian king & emperor in 900 until 905( when he was blinded) the last Italian emperor was Berengar I who was constantly the opposition in these civil wars until 924.

While Louis the child died young in 911 and the Germans elected their first non Carolingian king in Conrad I until 918 when he died and they elected a new king in Henry the fowler.

Henry was a saxon, the first non Frankish king. Henry is considered one of the great german kings and helped lay the foundation for Germany as a state.

But it's his son who is ultimately more important; Otto the Great. Which many historians will call the first Holy Roman Emperor. I disagree with that but it was a bloody mess before him.

Otto was crowned king of Germany in 936. He defeated the Hungarian invasions, put down civil wars in Germany and eventually in Italy.

In 961 Otto conquered Italy and was crowned king of Italy and emperor. This ended the first great interregnum where there was no emperor for 38 years. From then on, the kingdom of Italy and Germany with the imperial title remained connected.

In part two, we'll discuss Otto's imperial church system, the royal-noble power balance and why elected monarchy does not work well.