The Abyssal Services Department is an organisation responsible for maintaining the teleportation matrices used by players when they teleport through conventional methods. The Department is apparently tied into various human governments, presumably including major nations such as Misthalin, Asgarnia, and Kandarin. It is also likely that the group is connected to the Wizards' Tower.
When players teleport using basic rune-based spells, they typically are transported via established teleportation matrices controlled by the Abyssal Services Department. According to Mr. Mordaut's letter in Postbag from the Hedge 33, those that teleport using less conventional methods usually do so without the Department's knowledge.
When players were trapped in the Lost and Found random event, they were transported to a small pocket of Abyssal Space, caused by an error in the Department's matrices. When players left the event, it was the Abyssal Services Department that provided them with compensation for the inconvenience.