Short answers, pulled from the story.
Ultramontanism is a clerical-political position within the Catholic Church that places strong emphasis on the authority and prerogatives of the Pope in matters related to civil governance. It contrasts with Gallicanism, which held that civil authority over the Church was comparable to that of the Pope.
The term descends from the Middle Ages, when a non-Italian pope was called papa ultramontano, meaning a pope from beyond the Alps. After the Protestant Reformation, the direction of the term reversed in France, where ultramontain was applied as an insult to Catholics who supported papal authority over French civil affairs.
In July 1870, the First Vatican Council issued the Dogmatic Constitution Pastor aeternus, defining papal primacy and papal infallibility. It declared that the Roman Church holds a pre-eminence of ordinary power over every other Church and that all clergy and faithful are bound to submit to that power by hierarchical obedience.
The Old Catholics, known in German as Altkatholische, split from Rome in response to the First Vatican Council's declarations on papal infallibility and supremacy in 1870. They joined the Old Episcopal Order Catholic See of Utrecht, which had been independent from Rome since 1723, and grounded their rejection in the Declaration of Utrecht, the Theses of Bonn, and the Declaration of the Catholic Congress at Munich.
Ultramontanism has overshadowed ecumenical work between the Catholic Church and the Anglican Communion. The joint Anglican-Roman Catholic International Consultation published The Gift of Authority in 1999, finding agreement on the collegial role of bishops but leaving unresolved the distinction between a universal primacy exercised within a college of equals and one with actual universal jurisdiction.
The French philosopher Jacques Maritain, writing in the mid-twentieth century, contrasted the French model of laicite with what he saw as a more workable American arrangement combining sharp distinction and actual cooperation between church and state. He described the American model as an historical treasure and urged the United States not to let its concept of separation shift toward the European approach.