Principalities and Other Septs
Generational offshoots (cadet family lines) of the Royal House of Desmond received their own territories and titles - known as appanages of the royal house. Those MacCarthy Mór cadet branches which did not evolve to the MacCarthy Mór chief-of-the-name status, became chiefs-of-the-name of their own princely septs, i.e. MacCarthy Reagh of Carbery, MacCarthy of Muskerry, and MacDonough MacCarthy of Duhallow.
Because of their location, it was the MacCarthys of Muskerry and Carbery who ended up fighting the majority of the battles against the Normans - mainly the FitzGerald Earls of Desmond - while defending and expanding the Gaelic realms. By the mid-sixteenth century, the main line of the MacCarthys Mor had largely withdrawn to Kerry, so any modern claims that they are still entitled to the nominal overlordship of Carbery and Muskerry might be rejected by any extant descendants of these branches.
Read more about this topic: Kingdom Of Desmond