After Rome fell a series of german, french and gothic kings battled for power on the continent. They all had armies but what they desired was legitimacy, anyone can call themselves king but they need that kingly authority to remain in power and to become dominant. This was solved by becoming Christians, the pope who had legitimacy over these new kings of Europe simply by being respected and listened too would give his blessing to a certain King, like say Charlemagne and he would be the man. In other words Charlemagne got the iron throne from the pope but by doing so he had to accept the forsaking of the old roman line.

This enraged what we can see as the Targeryians (my spelling will be off bear with me) who respected the old but long dead emperors of the west. Empress Irene or the mother of Greek dragons (see: Greek Fire) was enraged and her and those after her would not stand for this, and they would invade Europe later on with a powerful army known to carry mercenary troops, (Byzantine army, Scandinavian mercenaries as well as Italian). She would see General Belisarius (that dick who loves his queen but then betrays her as he was also bad with women) with emperor Justinian (that dick who drogo kills) who was always way too ambitious and his wife who started very quiet and humble only to become the most powerful woman in the empire or Empress Theodora.

The pope can be seen as any king's Hand as he needed the king's support in troops and money as much as the king needed his backing and legitimacy. Pope Leo could be big daddy lannister as he was a savvy and wise man to see how he could cash in on his position to run the show and take on even the mighty byzantines with only a few words and support at the right time.

The lannisters would rule Italy out of what is france and Germany today. The Starks would be the english as they were always hated by the church for their independent and defiant kings, as seen later on in history when the pope excommunicated all of England. The byzantines would be Targeryians. The baratheons would be most comparable to the old line of Romulus Agustulus the last western roman emperor as he was the last legitimate heir to the throne, making his children and brothers all technically royalty and much more legitimate than Charlemagne and his father's before him. The Tully's I guess would be german and french today, and there were stil claims open and english and old roman nobles no doubt has shared blood.