So i always thought it was suspicious that during the mideval era the seat of the main sect of Christianity also happened to be in the same city as the capital of the Roman empire.(yes I understand in later years the administration was moved to medialonum/Ravenna) but the spiritual capital has always been Rome.
The pope holds the title "pontifex maximus" which was actually verbatim the same title held by chief preists in ancient Rome. I beleive ceasar even held it.
I get this gut feeling(for want of a better word) that the roman catholic church as an political entity in the mideval era was essentially the last remnant of the roman state, that overtime mutated and metamorphorised into its own political entity.
Or am I looking too much into this? And the papcy was just quarted in Rome becuase it was a major capital city in the founding days of christianity?
I"ll try to answer your questions.
It is certaintly not an accident that a universal capital like Rome became a major centre of the Christian movement. As Tacitus explained (with a condescending tone) every sort of new religious denomination appearing in the Empire found its way to Rome, and the ancient tombs discovered in Rome confirm this. When it comes to Christianity, we know that there was already a Christian sect in the city before Paul arrived there (at least that's what Paul seems to hint in his letter to the Romans).
It's important to understand that what eventually became the "Papacy" was initially just the office of the Bishop of Rome. But, given that Rome was the capital of the known world and that Paul and Peter were martyred there (tradition also held that they founded the apostolic see) Christians regarded Rome as a special place.
When the pagans became Christian, the fact that Rome was still nominally the capital of the Empire, amplified this. The Edict of Thessaloniki (380), which made Christianity the "state religion" of the Roman Empire , actually contains an interesting statement:
"We [Roman Emperors] believe what the Bishop of Rome believes".
But it should be noted that at that point Rome was "only" one of the five major centres of Christianity: Jerusalem, Alexandria, Constantinople, and Antioch were just as important. In the West, however, no city matched Rome's influence. So the Pope, in a now Christian empire, gradually claimed the title of Pontifex Maximus for himself, and the western Roman emperor abandonded this title (pagan in origins) in his favour.
More importantly, following the fall of WRE and the formation of the Papal States during the "barbarian invasions" up to the 8th century, the Pope could claim temporal rule over Rome, while the Byzantine (Eastern Roman) Emperor was in Constantinople and the ruler of the Frankish realms then became HRE Emperor only because of Papal coronation. It's in this framework that the Donation of Constantine is forged.
To see how the Papacy understood itself and its relationship to Rome it might be interesting to look at the text of the Donation of Constantine, which was proved to be a false document in the 15th century by Lorenzo Valla (but the Church continued to use it as a base of its claims even in the 16th and 17th centuries, considering that Valla's work was not accepted and then inserted in the Index of prohibited books):
We therefore decree that [the Pope] shall hold primacy both over the four principal seats of Antioch, Alexandria, Constantinople and Jerusalem, and over all the churches of God existing on all the earth; and that every pontiff of the Holy Roman Church shall be the highest and principal of all priests, and that according to his judgment all things pertaining to the worship of God and serving to strengthen the faith of Christians shall be regulated...[We] leave to the most beatified pontiff, our Father Silvestre, universal pope, and to the power and jurisdiction of his successors, our palace and all the provinces, places and cities of Rome, Italy, and of the western regions. We determine, by imperial decree intended to be valid in perpetuity...that they [the Popes] may dispose of [such possessions] and we grant that [such possessions] remain subject to the law of the Holy Roman Church. We have therefore considered it convenient to transfer and transport our empire and our royal authority to the eastern regions, and to build in the province of Byzantium, in a very suitable place, a city which will have our name, and to establish there the seat of our empire, because there, where the capital of the Pope and the Christian religion has been established by the heavenly emperor, it is not right that the earthly emperor should exercise power.
Obviously, the Eastern Churches and Emperor could not accept that, and this is also one of the reasons behind the schism of 1054, but that's another story.
To give another answer to your question, remember that there was not just one successor alone to the Roman Empire. The concept of successor state did not exist: there were numerous successors in different ways (ERE, HRE, Church). The papacy was one of them, via the possession of Rome.
Sources: ''Triumph of Christianity'' by Bart Ehrman (first part of the comment); F.CHABOD, Lezioni DI Metodo Storico, Laterza, 1992; Chiesa, enciclopedia Italiana (1931)