Many people nowadays think that simply because they are somehow related to Kamehameha, that is sufficient to claim the Hawaiian Throne or to think of themselves a royal. That is absolutely not true either in the traditional Hawaiian sense nor in the Hawaiian Kingdom's constitutional framework. In the West, lines of succession went from father to eldest son. That's because Western countries adopted ideas about succession from Christianity, which in turn adopted patriarchal ideas from Judaism and from Roman civil law. Hawaiian society was not patriarchal. All of the early Western and Hawaiian accounts agree that the mother's genealogy was of more importance than the father's genealogy. Women's ranks were fixed and in the age where women could have many husbands, paternity could be difficult to establish. Normally, the woman's highest ranking male husband could claim any of her children as his own. If a husband wanted to ensure that a child would be his, he would negotiate a schedule with the wahine and would have to pay an uku or tax to each of her other husbands and/or sometimes to her parents. Kamehameha had such an arrangement with Keopuolani. The same process would also be true of a woman who wanted to ensure that her children were of a particular father. A person's social standing within Hawaiian society depended on the rank of the mother. The rank of the mother served as the baseline in traditional Hawaiian society because no one could question maternity. The first source of mana always derived from women. titles could be inherited from the mother, but titles from the father side were more difficult to inherit. A person could improve his/her social rank through: having children of higher rank (hānau akua); through conquest (kūnaʻina); through acclamation (ololani); revolution (including usurping the throne); and, through deification (hoʻākua). Kūaliʻi for example was acclaimed as ruler of O'ahu by the 'Aha 'Ula who was struggling with a people's rebellion and civil war between the Lono and Kū line of chiefs, though Kūaliʻi came from a junior line of chiefs. 'Umi-a-Liloa was a low ranking chief though he was recognized as a son of King Liloa. The people overthrew his higher ranking brother Hākau and placed 'Umi on the throne. In both Kūaliʻi and Umi-a-Liloa's cases, they were regarded as usurpers by some but they solidified their positions through conquest and having high ranking children. Their successes as well as their devotion to the traditional akua legitimatized their lines and seemed to indicate the affection of the akua towards them. In China one had the "Mandate of Heaven". In Hawai'i you had the "Ka pili mahamaha o nā akua a me ka lehulehu" or the Affectonate Relationship of the Gods and the People". No ali'i could justify their rule without this "mahamaha" or affection. That was the way to maintain their mana.
Now fast forward to Kamehameha III. When he began the process of turning Hawai'i into a Constitutional Monarchy, he divided the ali'i into three major categories: royals; stewards or potential royals; and ali'i. Only the members of the Royal Family could be considered "royal" and these had to be confirmed in public decree with the approval of the Kuhina Nui and the House of Nobles. Higher ranking chiefs who had been loyal warriors and advisers to his father were considered to be stewards of the dynasty and as such some of their children were put into the Chief's Children School. The rest of the chiefs were ali'i and the bulk of the people that the king recognized as chiefs derived from kaukau ali'i, middle-lower level chiefs who owed allegiance to the House of Kamehameha. Even during the time of Kamehameha III, having ali'i blood was not a rare thing as the population was collapsing due to foreign diseases. It still is not a rare thing. With the implementation of the Hawaiian Civil Code, ali'i and royals who had children outside of their legally recognized marriages were not entitled to the same benefits as legitimate children. Kamehameha III, V, and Lunalilo all had known illegitimate children. King Kamehameha III had two very well known illegitimate children and the most well known was Albert Kūnuiakea. Though he was legally adopted by Queen Kalama, due to his mother's genealogy and the new legal code, Kamehameha III ensured that his successor would be Alexander Liholiho Kamehameha. Kamehameha III also set into motion a constitutional process that demanded that all ranks be publicly proclaimed during the lifetime of the sovereign and confirmed by the Hawaiian National Assembly in order to avoid civil war between rival heirs. When Kamehameha IV and Queen Emma had their son, Prince Albert Edward Kaleiopapa-a-Kamehameha, his rank had to be confirmed by the Privy Council , the Kuhina Nui, and the House of Nobles even though the son was legally legitimate. Kamehameha V had three very well known daughters from a Hawaiian commoner and one of these women served as a personal attendant of Queen Kapi'olani at the court King Kalākaua. Kamehameha V also stiffened Hawaiian nobility by declaring in 1865 that hereditary privilege in terms of titles and ranks was to be abolished and all ranks, titles and decorations awarded would be returned upon death to the awardee. When Princess Victoria Ka'iulani was born, her rank also had to be confirmed by the organs of state in the same manner as Prince Albert Edward Kaleiopapa-a-Kamehameha even though her mother was proclaimed a princess in 1875. In other words, she did not inherit the title of "princess". She was proclaimed a princess in her own right because hereditary titles and ranks were abolished decades earlier. Under Hawaiian tradition and under Hawaiian constitutional law, succession always depended on several factors. We still have a lot of ali'i descendants alive today, perhaps two out of three Hawaiians have some ali'i blood, but we legally stopped having royals upon the death of Prince Jonah Kūhiō.