Loved Robert Baratheon Jaime Lannister

Did Robert Baratheon earn the crown through his heroics or was it his right through succession?

"Tell me what right did my brother Robert ever have to the Iron Throne?" He didn't wait for an answer. "Oh, there was talk of the blood relationship between Baratheon and Targaryen, of weddings a hundred years ago, of second sons and older daughters. Nobody but the maesters cares. Robert won the throne with his warhammer."

A Battle of Kings - Catelyn II

That quote is always the starting point when it comes to how Robert got into the crown, and I think we all know the general overlay of Robert's Rebellion well enough. The answer I believe is both , but I don't think it could have happened any other way either.

Remember, Robert didn't start the riot! Sure, he was upset about the "kidnapping" of his promised Lyanna, but it was Rickard and Brandon Stark who went to King's Landing to demand justice, and Jon Arryn who shouted the banners first.

Rather than giving them a fair hearing, King Aerys had them brutally killed and after these murders asked Lord Jon Arryn to perform his previous wards, Robert Baratheon and Eddard Stark. Many now agree that the real beginning of Robert's Rebellion began with Lord Arryn's rejection and his courageous calling of his banners in defense of justice.

The World of Ice and Fire - The Fall of the Dragons: Roberts Rebellion

We know the end ... the rebels won and Robert was crowned king, even if he didn't quite want to.

Robert sat down again. "Damn it, Ned Stark. You and Jon Arryn, I loved you both. What did you do to me? You were the one who should be king, you or Jon."

"You had a better claim to your grace."

A Game of Thrones - Eddard VII

But why did Robert have a better claim? To answer that, let's think like a maester and ask what the Iron Throne represents ... It represents them Targaryen- Rule of a united Seven Kingdoms. So the ruler who sits on the iron throne should be a Targaryen.

Well, all true Targaryens were dead or in exile and the winners, at least, were something Had Targaryen blood in her veins ... it wasn't Tywin Lannister, it wasn't Jon Arryn, and it wasn't Eddard Stark. It was Robert Baratheon, of course. Robert's ancestry didn't even have to go that far back to his grandmother, Rhaelle Targaryen, to find her.

As they say, history is made by the winners and since Robert was the ultimate winner, the stories and songs will focus on his exploits. Robert was instrumental in the battlefield, but he also had the right blood in his veins to ensure a decisive and complete transfer of the Iron Throne to a non-Targaryen family.