Why did Eddard Stark bring Ice to King's Landing?

Question

I don't remember if it was explicitly confirmed , but the fact that Tywin gets his hands on Ice, while being in King's Landing, says that Eddard Stark must've brought it with him when he moved from Winterfell.

Bran, describes it as:

"Ice," that sword was called. It was as wide across as a man's hand, and taller even than Robb.

I wonder, would he need this giant sword? It's not a sword for actual fights, only used for beheading and almost impossible to use as a toothpick. As the Hand of Robert, would he plan to behead people himself?

Shouldn't he have left it at Winterfell so Robb, the acting Lord of Winterfell, could continue beheading deserters?

---

Thanks @Edlothiad with this confirmation that Ice is almost impossible to use in combat.

Asked if Ned ever used Ice in battle. George points out it was a greatsword, very large and cumbersome, a ceremonial sword for beheading people more than a fighting sword, so he suggests that it was "probably too heavy and clumsy" to use unless you're the Mountain.

Answer 1

Because he was going there as Hand of the King and given his job, he would be expected to sentence someone to death every now and then. And he believes that the man who passes the sentence should swing the sword.

Bran had no answer for that. "King Robert has a headsman," he said, uncertainly.

"He does," his father admitted. "As did the Targaryen kings before him. Yet our way is the older way. The blood of the First Men still flows in the veins of the Starks, and we hold to the belief that the man who passes the sentence should swing the sword. If you would take a man's life, you owe it to him to look into his eyes and hear his final words. And if you cannot bear to do that, then perhaps the man does not deserve to die. One day, Bran, you will be Robb's bannerman, holding a keep of your own for your brother and your king, and justice will fall to you. When that day comes, you must take no pleasure in the task, but neither must you look away. A ruler who hides behind paid executioners soon forgets what death is."
_{AGOT: Bran I}

But of course he could have used any sword to swing himself, it didn't have to be ice. But funnily enough, Lords of Westeros aren't as careful with their rare swords as one might expect them to be. King Tommen Lannister took Lannister ancestral sword Brightroar with him to Valyria even though one might have expected him to leave it at home. Lord Tarly uses Heartsbane in battle where it might be taken by a foe. Lord Corbray did the same.

It's probably because of the prestige of the sword. It has been carried by House Stark for centuries and is among the most famous swords of the Westeros. It is an heirloom of House Stark and is carried exclusively by the Lord Stark. Robb was not Lord Stark yet so there was no point leaving it with him. Must be noted however, Eddard Stark would sometimes let Robb and Jon handle it.

When Jon turned it sideways, he could see the ripples in the dark steel where the metal had been folded back on itself again and again. "This is Valyrian steel, my lord," he said wonderingly. His father had let him handle Ice often enough; he knew the look, the feel.
_{AGOT: Jon VIII}

Furthermore, Ned did not know that his time in office would be over so quickly. Jon Arryn served for almost the enitrety of Robert's reign and Eddard probably expected to do the same.

Eddard did eventually sentence someone to death (Ser Gregor Clegane) but given that his leg was hurt after his encounter with Jaime Lannister, he delegated the task of swinging the Sword to Lord Beric Dondarrion. Which was lucky or unlucky for him, Lord Tywin was waiting for him to take the bait and come to "swing the sword". Had he done that, he would have been arrested and exchanged for Tyrion Lannister. But by a stroke of fortune or misfortune, he didn't.

Answer 2

Heads would roll.

The Starks has a rule that the man who passes the sentence should swing the sword:

You send hired knives to kill a fourteen-year-old girl and still quibble about honor?" He pushed back his chair and stood. "Do it yourself, Robert. The man who passes the sentence should swing the sword. Look her in the eyes before you kill her. See her tears, hear her last words. You owe her that much at least."
_{A Game of Thrones - Eddard VIII}

This is the key idea here, although Eddard could've left the sword for Robb to pass the sentence, Eddard was still the Warden of the North and of higher rank than Robb (evidently). However, now as the Hand of the King he would certainly have need of the sword, and as such he would be swinging the sword himself, as opposed to letting the King's Headsman swing the sword.

This is highlighted when Lady is sacrificed for Nymeria's attack of Joffrey. Note this is also confirmation that it was Eddard that brought it down to King's Landing and not that it was taken later.

"Send for Ilyn Payne."
"No," Ned said. "Jory, take the girls back to their rooms and bring me Ice." The words tasted of bile in his throat, but he forced them out. "If it must be done, I will do it."
Cersei Lannister regarded him suspiciously. "You, Stark? Is this some trick? Why would you do such a thing?"
_{A Game of Thrones - Eddard III}

Eddard had indeed would've had time to use it during his time in office, had is death not come in such an untimely manner. While he would not have personally executed Gregor, he had commanded those he sent to execute him (thanks @Aegon), he set the tone for his later command over his position as Hand.

In the name of Robert of the House Baratheon, the First of his Name, King of the Andals and the Rhoynar and the First Men, Lord of the Seven Kingdoms and Protector of the Realm, by the word of Eddard of the House Stark, his Hand, I charge you to ride to the westlands with all haste, to cross the Red Fork of the Trident under the king's flag, and there bring the king's justice to the false knight Gregor Clegane, and to all those who shared in his crimes. I denounce him, and attaint him, and strip him of all rank and titles, of all lands and incomes and holdings, and do sentence him to death. May the gods take pity on his soul
_{A Game of Thrones - Eddard XI}

The sword was also ceremonial, and it is likely that Eddard would have had times where he'd have need of it.

Asked if Ned ever used Ice in battle. George points out it was a greatsword, very large and cumbersome, a ceremonial sword for beheading people more than a fighting sword...
_{So Spake Martin}