How did Robert manage to keep the seven kingdoms together following his rebellion? The 7Ks only became united under the Targaryen dynasty, so once that ended, wouldn’t it be more likely for them to break apart again after the Mad King’s demise? Why didn’t everyone suddenly start declaring independence again, instead of waiting until after Robert’s death?

There’s a couple different reasons:

  1. The Southron Ambitions/Rebel Alliance: Robert had already won the allegiance of the North, the Vale, the Riverlands, and the Stormlands. That’s half the continent right there, and even more so when Robert marries Cersei and gets the Westerlands as well. So it wouldn’t be seven kingdoms again, it would be one massive kingdom and a bunch of smaller states trying to avoid reconquest. 
  2. Institutional Inertia: The Seven Kingdoms have been part of one consolidated monarchy for almost three hundred years, less so for Dorne. That’s three hundred years with very few wars by historical standards, internal trade, law and order, all that good stuff. So people are going to be somewhat wary of going back to being warring kingdoms, especially after a rather bloody civil war which they lost.
  3. Targaryen Legitimism: even if the rest of the Seven Kingdoms wanted to start something, independence is unlikely to be the case because the Targaryens are still kicking around in Essos – as long as their kinsmen are available to be restored to the Iron Throne, the Martells aren’t about to declare themselves independent again.
  4. Internal Politics: This leaves the Reach, and they’re probably the most viable candidate for an independent state given their large army and economy, although it wouldn’t be easy trying to defend themselves on the Westerlands, Riverlands, Crownlands, and Stormlands borders at the same time. But the problem is that the Tyrell claim on Highgarden runs through the Targaryens – if the Reach isn’t part of Aegon’s realm, that claim isn’t good any more and the “Oakhearts of Old Oak, the Florents of Brightwater Keep, the Rowans of Goldengrove, the Peakes of Starpike, and the Redwynes of the Arbor” have every reason to claim the Oakenseat for themselves.

Regarding Steffon Baratheon’s mission to Volantis to find a bride for Rhaegar, do you think its possible he just botched the mission because he was already part of the “southron ambitions” alliance?

Here’s the thing about Steffon Baratheon…after WOIAF, I’m less convinced than I was before that Steffon was part of the Southron Ambitions conspiracy. After all, everything in WOIAF speaks to Steffon as having been super-tight with another power bloc:

Aerys and Tywin had known each other since childhood. As a boy, Tywin Lannister had served as a royal page at King’s Landing. He and Prince Aerys, together with a younger page, the prince’s cousin Steffon Baratheon of Storm’s End, had become inseparable. During the War of the Ninepenny Kings, the three friends had fought together, Tywin as a new-made knight, Steffon and Prince Aerys as squires.

By contrast, we learn absolutely nothing about any potential links to Jon Arryn, Hoster Tully, or Rickard Stark. Now, it’s possible that Steffon’s closeness to Aerys meant that he could see the growing madness, but that’s not really the impression you get with the whole trip to Volantis. (Maybe he blamed the Targs for his father’s death? I dunno.)The detail that bugs me is we don’t know why Jon Arryn was chosen to be Robert’s foster-father – was this due to a close relationship between Jon and Steffon or something else?

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So my current thinking – and I have to say, I feel 60-40 on this – the Baratheons weren’t supposed to be a part of the SA coalition: after all, they had close blood relations to the Targs, Steffon was personally close to Aerys, etc. Rather in a stroke of good luck/political nous, it was only after Steffon’s death and Robert becoming Jon Arryn’s ward that the SAs could count on having the Stormlands in their camp. 

Perhaps this explains why Hoster Tully reached out to Tywin Lannister for a marriage alliance. The SAs not being idiots, they could see that Tywin was on the outs with Aerys, and getting the second-most powerful man in Westerosi politics along with the might of the Westerlands for their power bloc could only help.