The Sorceror's Apprentices

Quick Walkthrough
# Talk to   in the   in   to learn about his master, Tarhiel.
# Retrieve the Journal of Tarhiel and his Scroll of Icarian Flight from his dead body north of Seyda Neen.
# Talk to   in the Great Hall of Ebon Tower Palace about Tarhiel and present his journal as evidence of his death.
# Inform his apprentices, Saturius and   in the Julianos' Tower, of their master's death.
# Return to Caros Cocceius to set up the 3 trials and then go inform the two apprentices about the trials.
# First trial: enchanting robes. Kelkemmello will win.
# Second trial: conjuration. If you do nothing, Kelkemmello will win and become the new master. You can goad him into summoning a Winged Twilight causing him to lose.
# Third trial: Kelkemmello will win and become master if you do nothing but if you give Saturius a Scroll of Icarian Flight he will win and become master.
# Talk to the new master in Julianos' Tower.

Detailed Walkthrough
Tarhiel's Death
To first get the Tarhiel conversation topic, you will have to talk to one of his apprentices,   and Kelkemmello in the   in Ebon Tower,  . Then you will have to go to   in Great Hall of Ebon Tower Palace to present evidence of his death. If you don't remember who Tarhiel is, he is everybody's favorite wizard that falls to his death when you walk north from Seyda Neen at the start of the game. Unfortunately, you're going to have to present his journal as evidence and chances are you didn't pick it up or sold it at the nearest store hours ago. Check the stores you would have visited when you started the game. It could be at Arrille's Tradehouse for all you know.

Once you present the journal to Cocceius, you will have the grim deed of informing his apprentices about the death of their master. You'll quickly learn that Saturius is the nice one, albeit less skilled. What Kelkemmello has in magic abilities, he lacks in character.

The Three Trials
Return to Cocceius and he'll discuss the three trials that the apprentices will have to go through in order to choose a new master sorceror for Ebon Tower. You'll have to trek back to the Julianos' Tower again to inform the apprentices.

After informing them, you'll return to the Palace to see the two apprentices next to Cocceius. Talk to him to start the trials.

The first trial will be an enchanting challenge where the two apprentices will have to compete to perform the best enchantment on a set of robes. Kelkemmello wins this one with ease as Saturius manages to create a robe that causes fire damage on the wearer, yikes!

The second trial will be a conjuration challenge. You can let Kelkemmello win this one and have him become master if you just let it play out but why would you do that? Saturius tells you that he is only capable of summoning a scamp whereas Kelkemmello can summon a daedroth. Tell him to summon something more impressive and he will summon a Winged Twilight that he can't control that the Palace guards will have to kill giving Saturius the win.

The third trial is a duel. You can allow Kelkemmello to win if you just let it play out but again, why would you want him winning anything? Talk to Saturius and give him a Scroll of Icarian Flight which you would have picked off Tarhiel's corpse. If you don't have one, there's one on the very top of Ebon Tower. I guess that's where he jumped from. Saturius manages to weaponize the power at reduced potency throwing Kelkemmello a few meters up in the air and falling down again causing him to forfeit.

You can talk to the new master back in Julianos' Tower to get your reward. Note that they will be higher up in the tower now from where you talked to them previously.

Quest Stages