I had this amazing game not too long ago. I was playing as Ronald Connington, starting just after Robert was crowned. More precisely I played him as a diehard Targaryen loyalist, determined to bring them into power no matter what. So he assassinated Robert, Stannis, Renly... Renly somehow was the hardest one, despite being a child, surviving several attempts and putting the whole thing on the brink of catastrophe. Stannis also had a daughter before he died so she had to be bumped off too. It was neither honourable nor good, but the Baratheons were extinct, and the one true king was free to take his place. Old Ronald could just cry for joy.
King Viserys III went over about as well as anyone but Ronald might have expected. Bad enough that he was, well, Viserys. He was also a Moonsinger. Within a few years every single kingdom in Westeros seceded, as did a few smaller lordships and the High Septon. It was like the Years of Blood all over again, made more ridiculous by the fact that Viserys, and his descendants, managed to cling on to one half of the Crownlands for decades after that, despite being in a near constant civil war with their few remaining vassals. The Targaryens were too weak to push them out of "their" countryside. The rebels probably didn't even have enough manpower to really besiege King's Landing.
Ronald was crestfallen and contrite, but he also had other problems. The Baratheons, before going extinct, put House Buckler in charge of the Stormlands. Now I have an irrational out-of-game hatred for House Buckler because Baratheons always leave this no-name dull boring House in charge of the Stormlands. I can't imagine a Connington was thrilled with it either - or the way they helped stab the Dragon in the back during the King Wars. Ronald tried to scheme against them from within (he actually was trusted and liked by them and granted a position on the council - not sure what it was, I think Master of Laws?), but had no success due to Storm King Ralph Buckler, the Old Buckler as I ended up calling him, being staggeringly popular with most everyone else in the realm. However, he was weakened by a failed war with the unquestionable post-Targaryen superpower: Willas Tyrell; and his enemies overthrew him, only to replace him with his son Selmyr, the Young Buckler. He was killed. Then his son Arstan became the Younger Buckler.
There were too many Bucklers to assassinate them all, and not enough takers for the assassination plan either. Attempts to fabricate a claim to the Stormlands and turn them into a force for law, order and the Targaryen way did not bear fruit either. And so Ronald fell upon a desperate gamble. One more attempt to fix at least some of the damage he unleashed and put the Stormlands under less despicable, more legitimate leadership. He declared for the Republic. And surprisingly, some of the other lords - namely Imry Wylde, the Old Buckler's left hand man, Master of Whisperers and High Lord of the Rainwood and Endrew Estermont, distantly related to the Conningtons - went for it too. At first the rebellion seemed sure to fail. Twice did Ronald's nephew, Quentyn Connington, a genius of warfare (Brilliant Strategist, Formidable Fighter, Organiser but still outnumbered and outmatched, march upon Storm's End. Twice did he fail to break the enemy - but he bled him and kept him occupied. And in the meantime, reinforcements kept arriving. Money was raised and sellswords hired. And even volunteers came forth. What's more, Arstan also found himself having to deal with an unrelated peasant rebellion and a Reachman invasion. He was beaten. The Free State (really City) of the Stormlands was declared. Ronald did not live to see this, though; towards the end of the war, he died and was replaced by his unpopular, syphilitic lunatic of a grandson, Devin (incidentally his father Ronnet Connington had a brief time at the tilt of the rebellion; before Ronald died, he was captured during one of the failed marches on Storm's End, and had to be rescued in a daring mission to prevent the Conningtons being forced to surrender).
Devin became the first Republican Storm King. Bucklers, Estermonts, Wyldes and Swanns shared power with the Conningtons. Soon back under the Old Buckler's leadership and still holding many of the borderlands they took durign their reign as well as Storm's End itself, the Bucklers schemed against the Republic with the assistance of Imry Wylde, who came very close to restoring his friend as an absolute Storm King (read: I savescummed there, just because I wanted to see if I could save the Republic; in the original timeline that magnificent bastard plus some bad luck completely ruined me beyond all hope of return). But the Conningtons schemed back and managed to hold on for long enough for Imry and Ralph to die of old age, after which point the Counter-Revolution fizzled out. As with all young republics, the feudal relics of nearby have tried to put it down or at least take advantage of its weakness to eat at its borders - especially the Reachmen. But Quentyn Connington, Commander of the Republic, had denied them quick and decisive victories to preserve the fighting strength of his forces for when it will really matter. They won those wars but they could not crush the Republic. The lesser Bucklers also were not subtle enough in their scheming and allowed the Storm King, in cooperation with High Judge Guliann Swann, to exile several of them to the Wall. Quentyn distinguished himself further by crushing Buckler uprisings and defeating a Tyroshi invasion.
In time the Republic became strong enough to fight, diplomacy and espionage having won over most of the Stormlords to its support. Willas Tyrell, fresh from crushing Garlan in a civil war, decided to feast on the Stormlands some more. But this time Quentyn actually faced him in battle - and since Willas underestimated him, the Reachmen came to rue the day they attacked us. Their armies were beaten separately time and again, before they could unite. Amazingly, the Tyrells were actually beaten and forced to pay reparations for their trespass. While Endrew Estermont (who has taken very well to the merchant prince life, one might add) succeeded Devin as the new Storm King, Quentyn became both Chief General and Head of House Connington. Popular and having many friends among the Republic's lords, once Endrew died Quentyn was the unstoppable candidate to succeed him. And he did more than that. He saw the chaos in the Crownlands and put a stop to it by conquering King's Landing (by then fianlly seized by House Throne who finished off the Targaryens). It was time for the Republic of the Iron Throne. And from there...
Well, as it happens, Quentyn finally died of old age not long after a closely-fought but ultimately failed campaign to conquer the North. But not before the Mallisters of the Riverlands were forced to bend the knee, and the Arryns in the Vale. The way was open for Westeros to be united again... even if, as it happened, it would be under an elected Buckler King. Biding his time like the old Ronald, Quentyn's son the young Ronald killed Ralph II Buckler and then seized control over the Republic. Justice, though crookedly, had prevailed.
Also while all of this was happening Lotho Antaryon, Daenerys' husband, and their assorted spawn, had worked to transform Braavos into a slaveholding monarchy, while occasionally trying to conquer parts of Westeros. And the High Septon relocated to Bramfort. The now-independent Faith of the Seven found the Faith Militant could be a double-edged sword when the cynical old bastard that set them free was overthrown by the Poor Fellows and replaced with a zealous simpleton after their own heart. Lastly, the Tullys didn't last long as Trident Kings; they were overthrown by Patrek Mallister, who went on to conquer the North as well and establish himself as the northern half of Westeros' answer to Willas Tyrell.