I believe it's usually the higher priest, one in practice the longest. but after changing religion, I think they have it all wrong, for example; a priest should never go it alone, it's been said and is in the bible that when 3 or more are present and praying then God is present.

No human alone can cast out demons. That takes the power of God. For an exorcism to work, the priest has to be very strong in his faith. If the Church decides it has a truly possessed individual on its hands -- one that requires an exorcism -- the next step is to appoint an exorcist to the case. This is often the same priest who performed the investigation, but not always. Traditionally, Catholic exorcists undergo very little specific training to aid them in their job. While they learn a great deal about the devil and the risks and manifestations of evil, exorcism itself is not a specialized area of study in seminary school. What they know, they know from their experience in the role of priest and from the Roman Catholic rite of exorcism, which is the official document detailing the prayers and steps of an exorcism. Things are starting to change, though. Official exorcists of the Catholic Church formed their own organization in 1992. The International Association of Exorcists holds biannual meetings in Rome and sends out a quarterly newsletter to its members. In the newsletter, exorcists tell of particularly difficult or interesting cases and swap "tricks of the trade" (Cuneo, 266). In addition, in 2005, Rome's Regina Apostolorum Pontifical Academy (a university connected to the Vatican) started offering a class on exorcism.