Online:The Covetous Countess

Quick Walkthrough
# Read the Tip Board in the Thieves Den and accept the listing that starts with "Esteemed Thieves." You may repeatedly click "Goodbye" until it lists the correct quest.
# Steal and launder the required items.
# Deliver the clean items to the client.
# Return to Kari in the Thieves Den.

Detailed Walkthrough
Read the Tip Board inside Thieves Den. A new message announces,

"Esteemed thieves, I need your help. My wealth is vast and my wants are few. What I cherish most is that which I cannot simply buy. Well-lived objects, near and dear to their owners, from all walks of life. It is my last pleasure. Details attached."

"Payment for stolen goods as requested will be rendered to the guild immediately, provided they have had all traces of ownership severed prior to delivery."

"No partial deliveries will be accepted."

You will need to find and steal three items of the types specified.  If you have previously completed quests which offer laundered or stolen shipments, you might already have the items needed in your inventory. If not, collect them by following the hints in your quest log. Once you have the needed items and have laundered them, find the patron, Countess Viatrix Celata at the given location. After she has accepted the delivery, return to Kari in Thieves Den to collect your reward.

The delivery locations vary based on the requested object types and the character's alliance as follows:



Note that these only refer to the location where you must deliver the items.  They can be stolen from anywhere, either via Pickpocketing, Murder, robbing Safeboxes, or looting other owned containers.

Notes
The type of the stolen items can be seen right under their names when you hover over an item in your inventory, for example:  . Note that the "Treasure Type" is listed as Cosmetics, Grooming items, meaning that this will work for either category.
The value of the item makes no difference to the reward. Thus, it is most cost-effective to launder white-level treasures for this quest, and sell anything green or above.
You don't actually have to steal or launder the goods in order to complete the quest, you merely need to have clean items of the correct category in your inventory.  This means items from the "Large Laundered Shipment" (quest reward) or even dragon loot can be used to complete the quest as it does not have the "stolen" description when it is acquired. 
If you reached your daily laundering limit on the respective character, you can also steal/launder the items on another character and then transfer it via the bank.
The "Cosmetics, Linens, and Wardrobe Accessories" version of the quest also accepts "Dry Goods" in addition to the listed contraband types.
For characters below level 50, the category is chosen by level rather than at random, depending on the level of the zone where the objects are handed in. So characters level 1-15 will always be asked for Games, Dolls, and Statues; 16-24 will always be tasked to steal Ritual Objects and Oddities, while characters level 25-30 will always be asked for Maps and Writings.
The level requirement seems to have changed. At level 31 it is possible to receive the Maps and Writings task. While between 25-30 Ritual Objects and Oddities was offered fairly often, and only Maps and Writings once.
If your desired quest (message always starts as "Esteemed thieves...") does not appear on the Tip board then you may select "Goodbye", rather than accepting whatever random quest is displayed.  Repeating this process will cycle through the RNG quest options, allowing you to quickly repeat Covetous Countess.

Quest Stages