Amans seems to have been a contender for the kingship of Carmelide (Cameliard), which he fought to reconquer while Arthur, King Ryons, and Serses were busy with each other. King Bors killed Amans in battle.
Vulgate VI makes them the king's daughters, and Amans in the Vulgate is probably Aniause in Malory, but Malory makes the relationships less clear. Vulgate's version is probably more coherent.
Amans entrusted all his land and men to the elder of his daughters, but she proved a bad ruler. So Amans expelled her and put the younger daughter in charge. As soon as Amans died, the elder daughter whent to war against the younger and succeeded in gaining most of the property.
When Sir Bors, on the Grail Quest, came to the younger sister's last remaining castle, he found the lady, although young and beautiful, poorly dressed. She prepared an elaborate meal for him; he ate only bread and water. She gave him the best chamber and a fine bed; he slept on the floor, but rumpled the bed to appear as if he had slept in it, out of regard for her feelings. In her castle, he had symbolic dreams which indicated the choices he should make the following day in Grail tests.
He listened to the debate of the two sisters, declared that the younger seemed to be in the right, championed her cause against the older sister's champion, Priadan le Noir, and won.
In the context of the spiritual allegory of the Grail Quest, King Amans symbolized Christ, the elder sister the Old Covenant, and the younger sister Holy Church, dressed in mourning for the sins of evil-doers. Amans and his daughters seem also to have had their own flesh-and-blood existence, independently of the allegory.
Amans, who appears in the Vulgate and is probably to be identified with Malory's King Aniause, took advantage of the war between Arthur, Ryons, and the Sesnes to attack Carmelide. Thus, Amans' land would most likely have bordered Cameliard. Since the area south of Cameliard is Bertilak de Hautdesert's (Bercilak) territory, and Bertilak seems to be more or less allied with the powerful Morgan le Fay, I would put King Amans' land north of Cameliard, between about the Mersey River in the south to about the mouth of the Ribble River (at Preston) in the north.
Knowing no other name for this territory, Phyllis Ann Karr use the name of it's king, as do I.