On the Loose

At the start of Act 3, you are requested by Meredith at the Templar Hall in the Gallows to track down 3 dangerous apostates (Huon, Evelina, and Emile de Launcet) and bring them back dead or alive.

Acquisition

Speak to Knight-Commander Meredith at the Templar Hall in the Gallows.

Walkthrough

Head to the Templar Hall through the Gallows and talk to the Knight-Commander. If you answer "I am no ally of yours" you will receive Sebastian: rivalry (+5).

If you are playing a mage Hawke, choosing the "I won't be used" response will result in Meredith pointing out that as an apostate, your continued freedom is at her sufferance.

Afterwards, you can talk to her assistant, Elsa, for information pertaining to the fugitives. Afterwards, you are free to chase them down. (There is The Enigma of Kirkwall in a room next to Meredith, on the candle next to the door).

Huon

To track down Huon, head to the Kirkwall Alienage in Lowtown and speak with his wife Nyssa, if Merrill is with you she will explain the situation to her. Nyssa will tell you that he will be returning the next night. Go into Merrill's house after doing this and then back to Lowtown at night to have him appear. Confront Huon, who will stab Nyssa and attack you with blood magic. Kill him. Upon death, he will drop the Boots of the Champion and Formula: Fell Poison.

Evelina

To track down Evelina, you just head to Darktown and talk to her adoptive children, Walter and Cricket. If you say you'll help Evelina, you receive Sebastian: friendship (+5). Otherwise you receive Sebastian: rivalry (+5). Enter the Sewer Passage a few steps to the north. Fight two waves of demons and shades in the first clearing. There is a trap (Simple, 10 Cunning - 50 XP) in the next hallway. The next clearing has more demons and shades. The top of the stairs has another trap (Complex, 30 Cunning - 150 XP). You will find Evelina, who turns into an abomination. Kill her. After the battle Walter and Cricket will talk about Evelina where you can choose to give them money (5). If you give the diplomatic response you receive Sebastian: friendship (+5) whether or not you give them money. If you give the humorous response and no money you receive Sebastian: rivalry (+5) while giving them money nets you no points. If you give the aggressive response and no money no points are given, while aggressive response and giving them money gives you Sebastian: friendship (+5). Evelina drops nothing, though there is a Design: Rune of Devastation in a nearby chest.

Later, you will receive Letter: A Messy Handwritten Note from Walter. (This does not seem to depend on giving them money or not.)

Emile de Launcet

To track down Emile de Launcet, talk to his parents in Hightown at night. You'll learn his mother gave him money to escape, but he is wasting it on alcohol instead and will be found at The Hanged Man during the day. After speaking with them, check the room in the north east part of the map which contains several chests, one of which holds a Qunari Sword (Dragon Age II).

Note: The treasure room has a single Master level trap, though the triggers are spread out so that it appears to be two traps. Disarming a single square however disarms the entire room and earns 250 XP. On the ps3 version there is a master switch to the left of the door, prior to entering, that will deactivate the traps.

Upon leaving the mansion you will be attacked by several Blood Mages, one group will head out of a hidden alley along the left wall, it has a Master level (40 cunning) locked chest unless it was discovered prior to this quest.

Once you confront Emile, you have the option to turn him in or let him go. If Isabela is with you, she can provide some comedic relief, especially if paired with Aveline. Anders also has extensive commentary to contribute, and other party members also have minor comments. Isabela, Aveline, Anders, Merrill, Varric and Fenris have paired comments to contribute as well. Letting Emile go results in Aveline: rivalry (+5), Sebastian: rivalry (+5), Anders: friendship (+10). Turning Emile in to the Templars but allowing him to spend time with his date nets Sebastian: friendship (+5), Anders: rivalry (+5), Aveline: friendship (+5). So long as Emile survives, his father will send you a letter with a reward.

Quest Completion

Return to Knight-Commander Meredith (inside the Templar Hall within the Gallows) to claim your reward and finish the quest. You should also return home to receive the letters from Elsa on behalf of Knight-Commander Meredith, and Guillaume de Launcet for additional rewards.

Result

The Apostates are apprehended and Knight-Commander Meredith is pleased, slightly depending on how you handled Emile de Launcet. If you choose to let Emile go and tell her he is dead, she will express doubt in your claims but will not act upon it.

If you place blame of the situation with the Templars when talking with Meredith at the end of the quest, it results in: Aveline: friendship (+5), Fenris: rivalry (+10). If you do not and Anders is in your party, he will do so. If Fenris or Sebastian are also in the party, they will comment on Anders. (it doesn't affect their approval) Telling him to be quiet will result in Anders: rivalry (+10). Agreeing with him will result in Anders: friendship (+10)

Rewards

1200 XP(quest completion)
Boots of the Champion (Mage), Boots of the Champion (Rogue) or Boots of the Champion (Warrior) - from Huon's remains
5 from Emile's father, via letter at Hawke's Mansion (from either turning him in or letting him escape)
5 from Elsa on behalf of Knight-Commander Meredith, via letter at Hawke's Mansion
Design: Rune of Devastation. (from complex chest at end of Evelina encounter)
Formula: Fell Poison. (from Huon's remains)

Trivia

Walter's voice (who looks older) is higher than Cricket's voice (who looks much younger).
Huon has a tattoo identical to the mark every casteless dwarf has.
According to dialogue said by Gamlen in Act 1, Leandra Amell was originally supposed to marry the Comte de Launcet, which is ironic considering Leandra tells Hawke that magic has always existed in the Amell line and that by her choosing a mage, she was "bringing more magic into the line, not less," which she believes is the reason her parents didn't approve of Malcolm Hawke.
If you allow Emile to spend time with Nella, head back to the De Launcet Mansion (at night) for a funny scene. The Drunk Patron in the Hanged Man will also talk about what happens to Nella.
Bringing Fenris, Varric, Isabela (or Aveline) with you on your first visit to the De Launcet Mansion will cause the characters to make short statements regarding the De Launcet family before leaving, characters will always make a comment so long as they are present, this can lead to your whole party making a comment, though they have no bearing on the story:

Varric: "(Copying the last words of Lady de Launcet) Oh, but ze hanged man! It eez so filthy! *chuckle*"

Fenris (Will only occur if Varric is present and has already made his comment): "It is filthy!"

Aveline: "Orlesians." This is said in a derogatory tone.

Isabela: "They are so Orlesian." This is said mockingly.