After the humiliation suffered by Charlemagne in 778 in Moorish lands, his son, the future Emperor Louis the Pious, who was King of Aquitaine back then, did manage to grab some land in what is now Catalonia. The host that the young Louis led over the mountains in 785 to take Gerona included many Visigothic noblemen, descendants of those who fled the initial Muslim assault on the peninsula in 711. They had found refuge in the Frankish kingdom, had closely collaborated with Pepin the Short in his annexation of Septimania back in 752 and seem to have settled en masse in these coastal areas in Southern Gaul, the region that soon came to be referred to as Gothia.

The Franks and Visigoths took the city of Gerona and a wide swath of land in the Pyrenees in 785 and Barcelona in 801. And Barcelona was as far as they got. Even if they wanted to press on to the Ebro, it was the Llobregat, a tiny river that flows into the sea by the Barcelona airport, that would remain the 'frontline' for the next two centuries.

Rather than annex the new lands to Aquitaine directly (and thus, into the Empire), the Franks set up a separate march there, as fortified buffer zones on important military frontiers in Carolingian Empire were called. There was a Breton March (against the Bretons), a Saxon march (against Saxons), a Danish March and so on. The march around Barcelona soon comes to be called the Spanish March, Marca Hispanica (starting in the 820s in the Annales regni Francorum). It was divided in several districts, each administered by a comes. Now, this word is usually translated into English as 'count', but these early comites were not counts in the sense that we normally give to this word. Originally, a comes (='companion' in Latin) was a nobleman who had the trust of whoever put him in that position and who was charged with administering those defence zones. They did oversee fiscal matters, too, collecting taxes and managing the royal rights over waters, mines, woods, pastures and so on and. But their most important task were military. They had to ensure the defence of the march and lead troops into battle.

Now, Barcelona was important because it still had those huge Roman walls. (It also had the only okayish harbour between Narbonne and Tarragona although, frankly, I don't really think the harbour came into Frankish considerations. But the walls certainly did.) Moreover, it was the southernmost place the Christians held, as I said above.

The city was sieged and taken by Guilhem of Toulouse, himself a comes of Toulouse and a cousin of Charlemagne. Guilhem places his eldest son, Berà, as the comes in Barcelona. Berà's mother was a Visigoth, so he had the support of Visigothic nobility, too. After some shenanigans Louis the Pious (who was the Emperor now) recalled him to Aachen in 820 and had him fight in a judicial duel. Which Berà lost, dying in exile two decades later. As this case shows, those Carolingian 'counts' did not necessarily stay in one place for life and could be easily replaced. The position was not necessarily inheritable either.

Now, Barcelona was an important 'county' seat, but not the only one. One person could hold more than one county. For instance, Berà was the comes of Barcelona, Gerona, Besalú, Conflent and Razès. He seems to have delegated the last two counties to his son Guillemò, who continued to govern there after his father's dismissal. Barcelona, Gerona and Besalú went to a certain Rampon, a Frank who had also held the county of Osona. After Rampon died 5 years later, the three counties went to Bernard of Septimania, another son of Guilhem of Toulouse born to his Frankish wife. Bernat had been instrumental in the intrigues that led to the dismissal of his half-brother Berà and had enormous influence over Queen Judith and thus over the whole court of Emperor Louis. In the civil war that followed Louis' death in 840 both Bernard and his kinsmen ended up executed. The fortunes of whoever held the counties across the Pyrenees were closely tied to whatever was going on at the Frankish court. It was only with the continuing disintegration of the Carolingian realm that the counts in Gothia managed to assert their independence and started passing their county seats to their elder sons rather than being appointed by some distant Frankish king. Now, the last count to be appointed by the Franks and the first one to pass the county on to his son was Guifré (or Wilfred) the Hairy. Already the comes in Urgell and Cerdanya from 870, in 878 he became comes in Barcelona and Gerona. It was also this guy who moved his HQ to Barcelona, making it the de facto capital of the march. He got badly wounded in a skirmish with the Moors in 897 and died a few days later, passing Barcelona, Gerona and Osona (a county he repopulated) to his son Guifré II. That guy was the last comes of Barcelona to swear fealty to a Frankish king. Anyway from now on the comes of Barcelona is an independent count, passing his domain to his own heir. Direct male descendants of Guifré the Hairy continued to rule over Catalonia (and later over Aragon, Mallorca and Valencia) until 1410.

Hope it helps