The initial pitch was for "House Of The Dragon" to be a miniseries that covered various important parts of the Targaryen history. Aegon's Conquest, Dance Of Dragons, the conquest of Dorne, etc. Whether they visit those other two things still who knows.
Timeline wise the thing that gets you closest to the Mad King is the Dunk & Egg stories, which are also in development. That would cover the childhood and reign of Aegon V, the grandfather of the Mad King.
Nah House of the Dragon from the very beginning was always a Dance of the Dragons adaptation.
GRRM pitched two shows to HBO when they asked him for spinoffs - The Dance, and a Dunk and Egg adaptation. Ryan Condal had previously met with GRRM and asked if he could develop Dunk and Egg. But HBO originally declined Dunk and Egg and instead tabbed Carly Wray to develop the Dance adaptation. GRRM and Carly could not agree on where to start the show in the timeline. George wanted to start earlier, Carly wanted to start later, so HBO next went to Bryan Cogman (who was still working on writing the final season of Game of Thrones) who developed his pitch but saw it get declined in favor of the Long Night prequel show by Jane Goldman.
GRRM still persisted in wanting to see the Dance adapted so he personally met his friend Ryan Condal for dinner and hired him on the spot to develop the Dance. They then met at GRRM's house, opened the book, argued about where to start, found a compromise starting point, broke the pilot together, wrote a series bible, and then took it to HBO.
GRRM has spoken several times about how HBO wasn't really listening to his ideas and desires at this point. HBO was hiring their own writers to develop shows completely independently from GRRM. For instance, he had no idea they were even developing the Long Night show at the same time they asked him for spinoff ideas, and was surprised to learn they had that in development, plus like 10 other shows they were kicking around. He's since said that many of the writers HBO hired had never even read his books, and that he didn't want to go through that, which is why he wanted Ryan Condal specifically.
Once HBO received the $30 million filmed pilot for The Long Night prequel (called Bloodmoon), they screened it for execs, canceled it because it wasn't up to par to be their big spinoff series, and ordered a full series of the Condal and GRRM created Dance adaptation, which they named House of the Dragon. Then Ryan went to Miguel to see if he wanted to come on board as co-show runner, since he and Miguel had worked together in the past and Miguel had name cache from his work on Thrones.
What Miguel has said is they could conceivably turn House of the Dragon into an anthology, meaning they keep the branding "House of the Dragon" as an umbrella for other Targaryen stories throughout their 300 year history in Westeros. But that isn't set in stone, he was speaking hypothetically about what they could do once they finish the story of the Dance. But that was never the initial plan. In fact, Aegon's Conquest got it's own pitch already - they were going to write Aegon the Conqueror as a drunk
One effort was a script about the destruction of the ancient Targaryen empire of Valyria by Max Borenstein (Kong: Skull Island), another was a take on the Dornish warrior queen Nymeria by Oscar winner Brian Helgeland (L.A. Confidential) and yet another — like much in this story, never before reported — was about Aegon’s conquest of Westeros and penned by Rand Ravich and Far Shariat (The Astronaut’s Wife). That script portrayed the William the Conqueror-inspired figure as a drunken lout.
A behind-the-scenes chronicle of HBO’s years-long campaign to franchise its biggest hit of all time, featuring warring pitches, an abandoned pilot, tackled controversies and the George R.R. Martin superfan who earned the keys to the kingdom.
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