Asquith is a world. The planet used to be part of the Outback while it was home to Sad King Billy’s Windsor-in-Exile kingdom. During that period, access to Asquith was a three-week trip from Parsimony via spinship. 
Although the planet's appearance is not described in detail in the Cantos books, one of its most impressive features was Mount Hillary, comparing in height to Mons Olympus on Mars, and to the “final mountain” on the Ouster orbital forest visited by the Consul alongisde Theo Lane and Melio Arundez. 
Asquith was first settled by the First Expansion immigrants from what once had been the British Isles on Old Earth. It was later brought into the WorldWeb, where it was considered a quiet, backwater world.
Sad King Billy only left Asquith after CEO Yevshesnky allowed him to recolonize Hyperion.
During the time of the Final Shrike Pilgrimage, Asquith was home to Glannon-Height royalist factions, and Emlem Harbrit was a commodities broken on Asquith with connections to the royalists, alongisde Diana Philomel.
Asquith was targeted as part of the first wave of massive attacks upon the Hegemony in the period leading up to the Fall. However, it was the only first-wave world that had a FORCE contingent in place. Because of the military presence, during the Fall, many ships translated to Asquith seeking refuge from the incoming attacks.
Asquith was government by a World Parliament. After the Fall, the Socialist Labor Workers’ Party won over the Parliament after much finger-pointing on the planet. 
A. Bettik worked on Asquith for the first 50 years of his life in service of Sad King Billy’s father before going to Hyperion 30 years before the kingdom of King Billy’s kingdom did, in order to make preparations for the incoming migration