Could you clarify the question?
If you are asking how a Chapel, Mission or parish are erected canonically, they are done so by the Ordinary of the Diocese or Territory. So a Bishop or other who is given charge of a territory by the Holy See is the person who erects it. A priest cannot of his own authority “set up shop” without the permission of the Ordinary. Nor can a priest hear confessions, preach, offer a public Mass without faculties given by the local Ordinary or his delegate, except under certain circumstances. Those are primarily that the priest is travelling from a diocese where they have faculties to another place, and are hearing the confessions or offering a private Mass for those who accompany him. Or if someone is in danger of death and another priest is not to be had.
So a priest, even one who is in good standing in his own diocese or order cannot come into another diocese or jurisdiction and just set up a chapel or parish. The SSPX and other groups do that, but even under old Canon Law they should at the very least contact the local pastor or Bishop and inform them that they are in the diocese and seek permission to establish a chapel.
At one point in history here in the USA, Maryland was the only Colony which permitted the public practice of the faith. After a Protestant majority outlawed the Catholic Church from owning property the titles of the Churches were given to groups of laymen, but this was an anomaly and the Ordinary was in the eyes of the Church still the authority that needed to be followed.