Here are spoilers for episode 1 of season 2 of House of the Dragon.
The first episode of the second season of House of the Dragon It starts with Rhaenyra Targaryen in mourning, for having lost a stillborn baby (Princess Visenya) and for the death of her second son Lucerys Velarion, who is killed by her uncle Aemond while trying to reach the Baratheons to recruit them to fight alongside to his mother.
Lucerys is attacked by Vaghar, the largest and most powerful dragon in the kingdom, and that leads to Rhaenyra to seek revenge, which ends with the first-born son of Aegon II being murdered in his own bed and in front of his mother and his sister who slept next to him (from what is said around the murder, we assume that the child was decapitated).
So not only is there a fight for the crown, the war is marked by revenge and the need for both Aegon and the Hightoweras of Rhaenyra (whose children are accused of being bastards in season 1), of eliminating each other’s heirs to protect their own family and their right to the throne.
The death of the son of Aegon II in the second season of House of the Dragon leaves him without a clear heir, while Rhaenyra She is in a complicated situation because many believe that, because she is a woman, she is not the legitimate heir to the throne. And the line of succession is somewhat tangled.
Rhaenyra Targaryen’s heirs
Jacaerys Velaryon
Jacaerys Velaryon He is the eldest son of Rhaenyra and Laenor Velaryon, although his real father is said to be Harwin Strong, because the prince does not have the characteristic white hair of the Targaryens or Velaryons. But Jacaerys was recognized by Laenor, who dies in season 1, and that makes him the heir to the throne and first in the line of succession after Rhaenyra.
Joffrey Velaryon
Joffrey He is the third son of Rhaenyra, but rose one position in the line of succession when his brother Lucerys was killed by Aemons. He was also recognized by Laenor Velaryon and with that became a legitimate heir to the throne, although he is beneath his elder brother.
Viserys II and Aegon III
Viserys and Aegon are sons of Rhaenyra and Daemon, and they do have the famous Targaryen look. During season 2 they are still very young, but they are also heirs to the throne and, with them, Rhaenyra has many more heirs than her brother Aegon II. And because they are so small, they are less likely to die in battle, although they could easily be attacked.
Aegon II’s heirs
Jaehaera Targaryen
The princess Jaehaera She is the daughter of Aegon II and his sister Helaena. She is twin of Jaehaeryswho is killed by two assassins hired by Daemon to kill the child as revenge for Lucerys’ death.
Jaehaerys was the heir to the throne, but his death changes things and makes his sister the main heir, at least until their father manages to find another heir.
Maelor Targaryen
Aegon and Helaena have one more son named after Maelor Targaryen, who arrives to become the heir to the throne a few years after the death of his older brother. Due to what happened to his brother, Maelor had to be protected to prevent the line of succession from ending.
House Blackfyre
Several Targaryen kings ascend to the throne after Rhaenyra and Aegon II, but conflicts continue and this eventually leads to House Blackfyre ascending the throne.
The house was founded by Daemon Blackfyre, the bastard son of King Aegon IV Targaryen. Daemon was recognized by his father and this led him to create his own house, from which several kings emerge throughout history. But the Blackfyre eventually died out and the house ceased to exist, which is why it is not mentioned in Game of Thrones.
