Francia Media, Italy

Under Carolingian in-laws, Italy reestablished a bit of an independent identity that had been lost when Charlemagne conquered the Lombards in 774.

But this became to be very complicated by the interests of the Popes, who wanted a strong protector but also one who would not desire the Papal enclave itself. A good protector could be honored with Imperial coronation, but a less than faithful one could find someone else called in against him.
The Popes were best served by external protectors – too distant to threaten Papal independence, but close enough to be called in against any threat.

In this era, only one King came in from Germany, Arnulf, but there was then considerable involvement with nearby Burgundy. Crowning the local Italian princes Emperor seem to have been abandoned after Berengar I, who was crowned in 915. Berengar blinded Louis III of Burgundy. Just when it looked like another Burgundian house (Arles) might make Italy its own, another Berengar took over (950).
This time the German King Otto I was called in, to marry the widowed Queen (Adelaide, of Lothair II), and assume the crown of Italy (951-952).
Berengar was left, however, with Italy as a fief of Germany. But he was not very obedient, and when Otto returned, newly victorious over the Magyars (955), he dethroned Berengar (961). Later he was crowned Emperor by the Pope (962).

This ended the existence of an independent Kingdom in Italy, which would not be revived in similar form until Napoleon. Now the German Kings would become the nearly permanent protectors and/or antagonists of the Popes. This also served to keep Italy split between North and South, with the South continuing to interact more strongly with Romania and Islam.

Kings and Emperors of Italy
Berengar I of Friuli                         888-891
Wido of Spoleto                               891-894
Lambert of Spoleto                        894-896
Arnulf, King of Germany             896-899
Louis III of Lower Burgundy      899-905
Berengar I                                            905-922
Rudolf II of Upper Burgundy    922-933
Hugh of Arles                                     933-947
Lothair II of Arles                             947-950
Berengar II of Ivrea                         950-961

Overthrown by Otto I