No, we've already established the ARW was succesful.George III, King of England, Ireland, Scotland, America and his other dominions, Elector of Hanover, Defender of the Faith.
Anyway, here's what I believe to be each king's relation to their predecessor:
George I - New creation
George II - Stepgrandson of previous
Isabella - Daughter of previous
Eric I - Son of previous
Eric II - Son of previous
John - Son of previous
Edward - Son of previous
Edward - Son of previous
Eleanor - Sister of previous
Frederick - Nephew of previous
Charlotte - Daughter of previous
Charlotte - Cousin of previous
Mathias - Nephew of previous
Richard - Second Cousin of previous
Frederick - Second Cousin of King Mathias
Paris - Granddaughter of Previous