system
Given the following post, respond as if you're commenting on Reddit:
human
[ASOIAF] Robert was made king because he was a distant relative to the Targaryans. What would have happened of he didn't have that relation but still won the Rebellion?
gpt
The rebellion was actually led by Jon Arryn. He started it when he refused to follow the Mad King's command and kill Robert Baratheon and Eddard Stark.

All three of them led their armies in important battles during the war and all three of them had their moment of glory. Robert got a lot of fame because he killed the crown prince, Rhaegar Targaryen, but that was only possible because Ned arrived with a force and saved him in the Stoney Sept. Both Ned, Robert and Jon Arryn were at the Battle of the ~~Bells~~ Trident, where Rhaegar was murdered.

After that, Ned went on to capture King's Landing where he found the Lannisters sacking the city and Jaime sitting on the throne covered on Aerys' Targaryen, the Mad King, blood. 

He could have claimed the throne for himself at that moment, or for Jon Arryn. He could've taken the knee and claimed Jaime was the king now, for he was sitting on the Iron Throne.

However, Ned had little interest in the crown, or in the south, and he considered Jaime a dishonorable man. Jon was already aging and Robert not only had killed Rhaegar, he was single, in his prime, with a shadow of a claim to the throne.

They made the smart choice. They married Robert to a powerful vassal house, the Lannisters, and used that weak claim (it came from his grandmother and, in Westeros law, that is pretty much the same as nothing) to give him legitimacy.

Doing that, Robert could rule with support of a vast majority of his vassal lords (5 out of 8). The Tully's of Riverrun had supported him during his war after marrying two daughters to Lord Stark and Lord Arryn, the Starks and Arryns were obviously not an issue and the Lannister had a Queen by his side. Since Robert controlled the Baratheons, the remaining houses being were the Greyjoys, the Martells and the Tyrells.

The Tyrells fought for the Targaryen's during the rebellion, but did the bare minimum. They had little interest in finding themselves in the wrong side of the table.

The Greyjoys rebelled. Not because they had a problem with Robert, or they supported the Targaryens. They simple saw an opportunity and tried their luck. It not only didn't work for them, it gave Robert an opportunity to unify the kingdom against a common enemy. Under Robert.

The Martells were the real problem. Rhaegar was married to one of them, and the Lannister butchered her and her children when they sacked King's Landing. By the start of the books, however, they have not made any moves against Robert.

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**TL;DR:** Robert was single, so they could marry him off to gain another ally for the throne and his weak claim was only an excuse to give their coup some legitimacy

*edit*: Rhaegar died in the battle of the Trident, not the Battle of Bells.