The family was founded by the marriage of the scions of two powerful families: Marie-France Tessier and John Harness Ashpool. After the two were married, Ashpool began construction of Freeside in high orbit due to the relatively relaxed laws governing construction.
The family became extremely successful financially, developing the attached space station, sponsoring human colonization of space, and acquiring a number of other firms which subsequently flourished. An ownership search on one of their subsidiary firms required tracing through four larger corporations, although a share of their common stock had not been traded on the open market for more than a hundred years.
Tessier and Ashpool had two children: “Jane” and “Jean”.
However, following the death of Marie-France, the family became extremely reclusive. Family members, including Ashpool, tended to place themselves in cryogenic sleep. At any one given time, only one or two of the children would be awake. They are also known for cloning their own assassins, “vat-grown” ninja who follow their orders without question.
The family brought a large number of antiques with them and tried to make them fit the orbital environment but failed aesthetically. A representational image presented to that effect is the Door. It is briefly mentioned that the door was ugly. It had been a beautiful door, but to make it fit the room, the Tessier-Ashpools had cut it down. This, combined with the fact that it was the only rectilinear part of the room, made it look ugly in the new environment.
Without telling her new husband, Marie-France embarked on a plan to create artificial intelligences and envisioned a future whereby the family and the AIs would create a sort of symbiosis to expand and run the family corporation and grant them a sort of immortality. Upon finding out about this plan Ashpool strangled his wife to death, leaving the plan unfinished.
Nonetheless, the AI known in the “Turing Code Registry” as Wintermute speculated over the years on a way of completing the plan. The culmination of Wintermute’s schemes constitute the plot of Neuromancer.
By the time of Neuromancer the family has become extremely degenerate and dysfunctional. The patriarch Ashpool spends almost all of his time in cryogenic stasis. A dissolute alcoholic and heavy drug user, when he is awakened for the final time he has sex with and subsequently murders a clone of his daughter prior to committing suicide. 3Jane Tessier-Ashpool is the only member of the family not to have fallen prey to such insanity since Wintermute apparently communicated with her and provided her with copies of her mother’s journals and plans. Nonetheless, she is described as “jaded” and is extremely disconnected from the world outside the Villa Straylight.