Talk to any inhabitant of Highcross to find out that Mirili is conducting some sort of research. She can be found walking around town or in her house. She is a Dunmer wearing blue robes and a ponytail.
Walkthrough
When spoken to, she'll tell the Hero that she is making a Taxonomy for everything on the Shivering Isles.
Answer 'Fascinating. Tell me more.', and she will give the Hero a rude reply. Get her disposition up to 60 or more and she will employ them as her helper. She will give a list of things for them to collect and demands that one must also tell her where one found them. This last detail is just plain talk since there is no need to do so. She is practically asking for almost all ingredients on the Isles but will give a little 
for each one.
Once they have brought her a number of the ingredients she will then start asking for help capturing creatures, starting with a Baliwog; then an Elytra, next a Gnarl; and a Scalon. To help, she will offer a few select command beast spells, based on ones Illusion skill.
Ingredients and locations
Here are the list of ingredients one need and their locations. Locations still pending. Beware, she will not accept stolen items.
- Alocasia Fruit - can be found all over the island, specifically in the Halcyon Conservatory.
- Aster Bloom Core - can be found on the wall dividing Split into its two halves.
- Black Tar - can be found in the cave involved in the side quest searching for the fork. It is on a table in a basket near a chest in Hardscrabble Camp. The tar can also be found on the Strange Door before entering the isles.
- Blister Pod Cap - found on the Strange Door
- Congealed Putrescence - found on the Strange Door.
- Letifer Orca Digestive Slime - Can be found around The Fringe.
- Elytra Ichor - can be found on Elytra corpses.
- Flame Stalk - can be found around Bliss.
- Fungus Stalk - can be found on the Strange Door before entering the isles.
- Red Kelp Gas Bladder - found on the Strange Door before entering the isles or along the coast of Dementia.
- Gnarl Bark - from Gnarl Corpses.
- Grummite Eggs - from Grummite corpses or Grummite Hatcheries (Knotty Bramble).
- Hound Tooth - from Skinned Hounds.
- Hunger Tongue - from Hunger corpses.
- Hydnum Azure Giant Spore - found on the Strange Door.
- Water Root Pod Pit - can be found at Fellmoor.
- Rot Scale - northeast of Runoff Camp on a waterfall on the edge of the island and in most caves.
- Scalon Fin - from Scalon corpses.
- Screaming Maw - can be found inside most caves.
- Bone Marrow - from Shambles corpses.
- Swamp Tentacle - found around The Fringe.
- Thorn Hook - can be found in Blackroot Lair.
- Void Essence - on Flesh Atronach corpses.
- Watcher's Eye - can be found inside the Knotty Bramble.
- Withering Moon - can be found inside most caves
- Worm's Head Cap - found on the Strange Door before entering the Isles.
Trivia
- Many of the ingredients needed can be located in the two gardens and the royal throne room in Sheogorath's palace.
- If for whatever reason, one does not want to complete the quest, one can simply kill Mirili Ulven to end the quest.
- Some of the items needed can be found on A Strange Door before entering the isles, if one plan on doing the quest just grab these beforehand.
Bugs
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This section contains bugs related to Taxonomy of Obsession. Before adding a bug to this list, consider the following:
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- For some reason, if Mirili goes into her house to fetch the reward money, she may become stuck, forgetting to go outside and refusing to acknowledge when the Hero has brought her any new alchemical samples or animal specimens to examine. The quest can be continued simply by attacking her and going outside, as she will follow the Hero outside. A high disposition with her is recommended, as otherwise she will not stop attacking the Hero if they yield until they have paid off the small bounty they have obtained for assaulting her.
- For some reason, if one brings a baliwog outside of her house and waits until she is out, she may simply run away from the baliwog, if it is hostile.
- Fix: paralyze Mirili and let the baliwog get close to her. When she is unparalyzed she may paralyze it, if not paralyze her again until she does. This will however, garner a small bounty for assault.