Who holds the seats of the other eleven apostles today?

The bishops do. The office of apostle as such ceased with the death of the Twelve. What continues is the episcopate they established, so every validly consecrated Catholic bishop, not one man per apostle, is a successor of the apostles. The question assumes that each apostle had a personal chair that has to be occupied by one man in each generation, the way the chair of Peter is. That is not how the New Testament sets it up, and it is not how the early Church understood it. Look at what the apostles actually did. They did not clone themselves. They ordained bishops and handed the churches over to them. Paul left Titus in Crete "that thou shouldest ordain priests in every city, as I also appointed thee" (Titus 1:5). Notice the chain of command built right into the sentence: Paul could not command Titus to do that unless Paul was above Titus, and Titus could not do the ordaining unless he was above the men he ordained. That is how the Church was organized from the beginning. Timothy was given the same charge in Ephesus, and Paul told him to guard the deposit (1 Timothy 6:20; 2 Timothy 1:13-14), not to guard it as an apostle but as the man the apostle put in place. The first generation after the apostles says exactly the same thing. St. Clement of Rome, writing around 80 AD while the Apostle John was still alive, says Christ was sent from God, the apostles from Christ, and that the apostles, foreknowing there would be strife over the office of bishop, "appointed those who have already been mentioned, and afterwards added the further provision that, if they should die, other approved men should succeed to their ministry." St. Irenaeus around 180 says that the churches everywhere can trace the men "instituted bishops by the Apostles, and their successors to our own times," and then he demonstrates it with Rome: Peter and Paul founded the church there and "handed over the office of the episcopate to Linus," then Anencletus, then Clement, then Evaristus, and so on. St. Ignatius of Antioch around 110 puts it in one line: "You must all follow the bishop as Jesus Christ follows the Father, and the presbytery as you would the Apostles." The bishop is not an apostle. He stands in the apostle's place. So the apostolic office as such is finished. The reason is doctrinal, not organizational: public revelation closed with the death of the apostles. An apostle was an eyewitness of the risen Christ, commissioned directly by Him, and capable of receiving and promulgating new public revelation. A bishop can do none of that. All the bishops may do is guard the old revelation. Once revelation was complete, the office that existed to deliver it had done its work, and what remained was the office that exists to protect and transmit it. Then why does Peter's chair continue when the others do not? Because Peter's was never merely the personal office of an eyewitness. It was the office of the keys and of the rock, given to Peter for the government of the whole Church, and an office given for the permanent government of a body has to be permanently filled. The apostles themselves showed us the principle when they replaced Judas. Peter cited Psalm 109:8, "his bishopric let another take," the Greek being ten episkopen autou, the office itself, and Matthias was elected to it. They did not do that for James the Greater when Herod killed him in Acts 12. Judas's place was filled because the Twelve had to be twelve for the foundation; after that, the apostles stopped replacing themselves and started appointing bishops instead. What about the ancient sees? Antioch, Alexandria, Jerusalem, Ephesus and others really were founded by apostles, and their bishops really do sit in a line that goes back to an apostle. Rome is preeminent among them not because it is older but because it is Peter's. The other sees continue as bishoprics with their own dignity and their own apostolic pedigree; they do not continue as apostolates. And the bishop of a diocese founded last century in Nebraska is just as much a successor of the apostles as the patriarch of Antioch, because what he received in consecration is the same apostolic office of teaching, governing and sanctifying, passed hand to hand from the Twelve. So the short version stands: the successors of the apostles are the bishops. All of them.