Well, one of the reasons of Otto II being in Italy at this time was his empire was particularly troubled, and his death his going to make things worse.
First, who would take the tutelage (rather than regency) of Otto *III (not the historical one, but his elder brother that was still alive at this time).
His mother, Teophano? That's the logical outcome, but german nobles aren't going to like that at all : a foreigner, more or less symbolic of imperial ambition of ottonids...
I wonder if she would be able to gain to her cause enough nobles to enforce it : I would tend to think that after a while some great german noble would be the tutor de facto, if not de jure.
Adelaide, the mother of Otto II, is a far likely choice : she would be better accepted by german nobles, and depsite probable compromises (that could really delay imperial expension and authority at the benefit of great nobles), could hold the tutelage more easily.
Anyway, whoever he/she is, it's gonna be hard :
- Slavic and Danish attack could risk to transform themselves in conquests
- Most likely revolts of german and italian great nobles, especially if Theophano take the tutelage. You may even see the comeback of Henry II of Bavaria (not that I think this eternal challenger could actually win entierly, but he could enforce a reduction of imperial authority)
- Frankish intervention (see below).
the carolingians never really accepted the loss of Lotharingia and may try to swallow it up entierly during the unavoidable crisis (slavic raids, danes invasions, likely german revolts) instead of accepting only a part of it.
It could actually increase their authority face to Robertians, and the tentative of Hugues II to takeover the royal title could be butterflied in this case.
On the other hand, a failure of Lohtaire against an empire in crisis, could mean the establishment of a robertian dynasty in France, and then pretty sure the kingdom would know troubles of its own.
- Saracenic raids could use this to be more devastating, and the imperial victory in Italy against these could be more hard if not butterflied.
The empire is gonna make concessions in order to prevent being defeated on all fronts. Political (reduction of imperial power), territorial (probable loss of Schleswig, possibly more at the benefit of Danemark; maybe parts or if really unfortunate all of Lotharingia; maybe but unlikely, slavic marches).
These concession could be of course only temporary, but I think the neighbours of the Empire would benefit them more than german or italian nobles.