There dwelt at Reykjaholar a man named Thorgils, the son of Ari, the son of Mar, the son of Atli the Red, the son of Ulf Squint-Eye, the first settler at Reykjanes. Thorgils' mother was Thorgerd the daughter of Alf of Dalir. Alf had another daughter named Thorelf, who was the mother of Thorgeir the son of Havar. Thorgeir, therefore, had a very strong backing through his connections, for Thorgils was the most powerful chief in the Vestfirding quarter. He was very open-handed and gave hospitality to any free-man for as long as he would. There was consequently always a crowd at Reykjaholar, and he lived in great grandeur. He was both kindly and wise. Thorgeir stayed with him in the winter and went to Strandir in the summer.

After slaying Thorgils the son of Mak, Thorgeir went to Reykjaholar and told Thorgils Arason what had happened. Thorgils told him his house was open to him. "But," he said, "they will press the matter vigorously, and I am most unwilling to involve myself in difficulties. I will send a man now to Thorsteinn and offer him blood-money for the Thorgils affair; if he will not accept it I will not adopt any violent measures."

Thorgeir declared that he would submit to his wisdom. In the autumn Thorgils sent a messenger to Thorsteinn Kuggason to try and arrange a settlement. Thorsteinn was very disinclined to accept any money in atonement for the slaying of Thorgils, although for the others he was willing to follow the advice of men of counsel. Thorgils on receiving the report of his messenger called Thorgeir to a consultation with him and asked him what support he thought was proper. Thorgeir said that if a sentence of banishment were passed upon him he would go. Thorgils said that his resolve would be put to the trial.

There came a ship into the Nordra river in Borgarfjord, and Thorgils secretly took a passage in her for the two foster-brothers. The winter now passed, and Thorgils heard that Thorsteinn and his party had assembled in great force for the All-Thing and were then in Ljarskogar. So he put off his departure, intending that they should arrive from the North before he came up from the West. So it came to pass. Thorgils and Thorgeir then rode towards the South, Thorgeir killing one Boggul-Torfi on the way at Marskelda and two other men named Skuf and Bjarni at Hundadal. Thormod sings about this affair in his Thorgeir's drapa:

Thorgils settled for the slaying of Skuf and Bjarni there and then in the dale, and was delayed by the affair longer than he intended. Thorgeir embarked on the ship and Thorgils went to the Thing, where he did not arrive before they were proceeding to judgment in Thorgils Maksson's case. Asmund Longhair then called for the defence. Thorgils appeared before the court and offered blood-money in atonement on condition of Thorgeir not being sentenced to banishment. He endeavoured to meet the charge by pleading that finds in the Almenningar were free to all. The question whether this was a valid defence or not was referred to the Lawman, who at that time was Skapti. He upheld Asmund's view on account of their kinship together. He declared that this was indeed the law in the case of men equal in position, but that a bondi had precedence over a vagrant. Asmund further urged that Thorgils had offered to share the uncut portion of the whale with the foster-brothers when they arrived. The defendants were non-suited on that point. Then Thorsteinn and his party pressed their suit resolutely and said they would not be satisfied with any sentence short of banishment upon Thorgeir. Thorgils saw that no choice was left to him but either to call up his men and try to carry his case with violence, the issue of which would be uncertain, or else to submit to the sentence demanded by the opposite party, and since Thorgeir was already on board his ship Thorgils had no desire to press the case further. Thorgeir was banished, but Thormod was discharged upon payment of blood-money.

Asmund and Thorsteinn gained great glory by this case. The men rode home from the Thing. There were some who said that Thorgils had not taken much trouble in the case, but he paid little attention and let them say what they pleased.

When Thorgeir heard that he was banished, he said that if he had his way, those who had brought it about should be repayed in full before it was over.

There was a man named Gaut, called the son of Sleita, a kinsman of Thorgils Maksson. He was intending to travel in the same ship with Thorgeir, with whom he was on very bad terms, and frowned on him. The traders thought it would never do to have them both together in the ship. Thorgeir said he did not care what Gaut did with his eyebrows. Nevertheless they decided that Gaut should leave the ship. He went into the northern districts and for that time nothing happened, but the affair brought about a feud between them which broke out later.