The lineage and descendants of Arthur is an area wrought with difficulties: patriotic (people want to show he was a real person); empowered (people want to show they are descended from him*); political (people want to show he was from their area); and finally poetic (everyone has a different Arthur). Different genealogies have been offered for him by different set of writers: the early mediaeval; the Normans; the later Romantics. Much of the field is distorted by the works of Geoffrey of Monmouth (See Other Works) who probably did some heavy-handed editing and interpolation from earlier sources.
Attached to one Welsh version of Geoffrey's "History of the Kings of Britain" is a genealogy which seems to insert Arthur, on his father's side, into the kingship of Cornwall/Devon1 (the Mostyn Manuscript 177 genealogies; late 13th C.). The names on this are in Welsh, though it is unclear if this is copied from an earlier source or not2 . On his mother's side, much of the information comes from a separate manuscript (Vitellius C.IX). More generally, it is usually accepted that information found in tales from Wales, Cornwall and Brittany that have older linguistic traits and that contain information not found in Geoffrey are drawn from an older and more reliable tradition3.
Given all this, here's the lineage of Anir. Special mention is particularly due to the work of Bromwich* in the construction of this.