Middle Francia was created in the treaty of Verdun in 843 which cut Francia into three parts; after several revolts and wars between the three sons of Ludwig (son of Charlemagne) and their father. The ruler of the middle part was to be Lothar I. (also inheriting the title of emperor) and shortly before his death he divides his Lands again between his three sons in the Treaty of Prüm in 855. The north went to Lothar II., Italy (or the part of Italy that had been part of Francia) to Ludwig II. and the Provence and Burgundry to Charles. But this situation also wasn't destined to keep for long and after the deaths of Charles and Lothar II. there was another treaty in 870 this time named after the city of Meersen. In it the former Middle Francia was again divided between East and West Francia and the Kingdom of Italy. Some maps to illustrate the situations better:

• Treaty of Verdun (https://commons.wikimedia.org/wiki/File:Treaty_of_Verdun_English_(2).png (I can't get the formatting for this one right))
• Treaty of Prüm
• Treaty of Meersen

So you could call Italy the third successor state (some lands actually changed hands again in the fourth treaty (Ribemont) in 880), if it weren't for Otto I. who was king of the Germans and conquered the kingdom of Italy in the 950s again unifying it with the former East Francia after the last descendant of Charlemagne in Italy had died.

So, even though you can definitely spot certain later countries or regions when you look at Middle Francia on a map, it was in effect not very long lived and split up between the other two kingdoms with the same heritage.