If a tree falls in the godswood and nobody is around to hear it, did it ever really fall? That's what I would equate with what the Iron Throne has become in Game of Thrones's sixth season. No one really cares about the Iron Throne anymore. There's a burgeoning war in the North. Daenerys Targaryen has burned down the patriarchy and is ready to conquer the West. Then there's the horde of hungry wights headed South. King's Landing is no longer the morally bankrupt center of this tale of ice and fire.
That's probably why no one has even noticed that the Baratheon lineage is one dead king away from total extinction. And let's face it: Tommen Baratheon, the First of His Name, will die. It's just a matter of when. But what happens when Tommen succumbs to his mother's prophecy? Who will sit on the Iron Throne? It's a nebulous situation.
In the books, it's a little more black-and-white. Myrcella, Stannis, and Shireen, three rightful successors to the throne, are still currently alive in George R.R. Martin's narrative. However, the show has clearly done away with the Baratheons. (Technically, Joffrey, Myrcella, and Tommen aren't even Baratheons, but for whatever reason no one has ever contested their legitimacy as the children of King Robert Baratheon.)
With the clock ticking on Tommen, we need to start thinking about the next heir to the Iron Throne. Now, as Robert's last remaining bastard, Gendry would be the next in line. (He's more legitimate than the throne's previous two occupants.) But there's only one problem: Gendry is a bastard. Unless Tommen legitimizes Gendry as a Baratheon — and he would never do that — then there's no way Gendry is sitting on that throne.
So that rules out the Baratheons. (See, Robert? This is what you get for usurping the Targaryens.) Who's next in the line of succession? Since Margaery hasn't been lying with Tommen in the marriage bed, a natural-born heir is unlikely. So we must look elsewhere for our golden goose. One astute Redditor dug through the serpentine Baratheon family tree and reached an interesting conclusion: Cersei Lannister.
In order to understand why Cersei would be the heir to the throne, you have to go all the way back to Robert's great-great-great-great-grandfather, Corwen Baratheon. Corwen had six kids -- and one of them married a lord named Mathin Lannister, who just so happened to be Tywin Lannister's great-great-grandfather. Since Tywin is dead, Jaime is a sworn member of the Kingsguard who has never shown any interest in being king, and Tyrion is still a wanted man in King's Landing, that leaves Cersei.
However, Westeros has never allowed for female rulers before, so her reign will undoubtedly be disputed. Not to mention, she's not in the Faith's good graces at the moment. It's doubtful they would even allow it. Unless she somehow got rid of them. And wouldn't that be horribly poetic? Cersei, distraught over the death of her last son, has to sit on the very throne that caused this mess in the first place? Still, Cersei seems like an unlikely candidate.
There's no legitimate heir to the throne, and honestly, it doesn't matter. The secret battle for the Seven Kingdoms is over. It's been usurped by something greater. Winter is coming, and playtime is over. It's clear that whoever will sit on the Iron Throne next will have to take it — either by fire and blood or ice and darkness.