The Icelandic conversion is the one case in northern Europe where the change of religion was settled as a point of law by an assembly that could have gone either way. Around the year 1000 the Althing at Thingvellir faced a split between a Christian party with royal backing from Norway and a heathen majority. Rather than fight, both sides agreed to be bound by the ruling of a single arbitrator, and they chose Thorgeir Ljosvetningagodi, a heathen priest. He is described as lying under his cloak for a day and a night before giving his judgment: all should be baptised and hold one law, while private sacrifice, the eating of horseflesh and the exposure of infants would be tolerated for a time. Islendingabok, written more than a century later by Ari Thorgilsson, is the source.
That settlement had a consequence nobody planned. Because the old religion was not defeated in a war and its practitioners were not treated as a conquered enemy, Icelandic Christian scribes had no compelling reason to destroy the material. They wrote it down instead. The Poetic Edda, the Prose Edda compiled by Snorri Sturluson in the thirteenth century and the family and legendary sagas are the reason a coherent account of Norse mythology exists at all, and every reconstruction of Germanic religion elsewhere in Europe leans on Icelandic manuscripts written by Christians two hundred years after the conversion.
The Lutheran Church of Iceland is established and named in the constitution, and is funded by a parish charge collected with income tax and allocated to whichever registered body a taxpayer belongs to. Membership has fallen well below the Nordic norm and the number of registered religious and life stance organisations has grown.