House Stark has had a bad time overall in Game of Thrones and A Song of Ice and Fire, their numbers considerably thinned since the series started. Many in Westeros think that House Stark is nearly extinct, with Sansa as the last living member (although, in fact, she is not). Truth is, House Stark is probably going to be okay… but other houses, not so much. We’re going to take a look at each of the Great Houses, and I think you’ll be surprised how vulnerable some of them are.

Which Great Houses Might Go Extinct By The End Of A Song of Ice and Fire?

There are nine Great Houses in Westeros,: Stark, Arryn, Baratheon, Tully, Greyjoy, Lannister, Tyrell, Martell, and Targaryen. Several of these are not currently in power—Targaryen is obviously out of the immediate picture, but the Tullys and Starks have both lost their official supremacy in their respective regions. But we can worry about that later; they’re still Great Houses. By my counting, three are in danger of extinction, and two have other big problems going on. Let’s take a look.

Great Houses Who Aren’t In Trouble

Four houses have nothing to particularly worry about: Tully, Greyjoy, Tyrell, and Martell. In the TV show, Tyrell has problems since Mace’s only children are Margaery and Loras, but in the books, Willas and Garlan Tyrell stand before either in the succession. Edmure Tully is a captive of the Freys, but he’s married and his wife stands to bear an heir… he may be a pawn of another house, but the Tullys aren’t going extinct. Martell is doing just fine, and there are so many goddamned Greyjoys they don’t have to worry about these things for years. But now for everybody else…

The Lannisters

House Lannister is not, strictly speaking, in trouble, but the dominant line is. This has long been known, and was a major source of dissatisfaction for Tywin. Jaime is in the Kingsguard and unmarried; he has no legitimate issue. Cersei’s children are not Lannisters, but Baratheons; even if their bastardy were fully accepted, they would not become Lannisters, just bastards. Tyrion doesn’t look likely to have any kids, certainly not legitimate ones, and he’s half a world away.

None of the three look terribly likely to have legitimate issue, meaning the dominant line of House Lannister would pass through Kevan and his sons. In the books, of course, Kevan is (spoiler alert) dead, but his son Martyn Lannister is not. Lancel is a jerk and won’t have kids, but Martyn can carry on the line, and he has a sister who could marry matrilineally and carry on the line. Tyrek Lannister, if he’s still alive, could also continue the House name. But the dominant branch of Tywin’s kids? That’s tough sledding.

Stark

As said above, House Stark is not in dire trouble. Robb is dead, Bran is never coming back, and Arya may not either, but Rickon is alive and in hiding, and the most likely bet to continue the House. In his absence, Sansa could too. Don’t worry too much about the Starks—they’ll have their comeuppance.

Arryn

Arryn is generally considered the most likely of the Great Houses to go extinct. Jon Arryn had immense difficulty in having children, and the other heirs to the family all died during Robert’s Rebellion. Robert Arryn, our Sweetrobin, is… not the most promising of candidates to continue House Arryn. Should he die, House Arryn in the dominant line, one of the oldest and purest Great Houses in Westeros, comes to an end. Harrold Hardyng, a descendant of Jon Arryn’s sister, would inherit the Eyrie, and he carries the Arryn blood, but the family name would pass away.

Baratheon

Believe it or not, House Baratheon is at great risk. Strictly speaking, it has four living members; technically, it only has two. King Tommen Baratheon and Princess Myrcella Baratheon are both bastards. Both are also prophesied to die before Cersei, presumably without issue. Not that their children would be true Baratheons anyway, but they’d bear the name.

Renly is dead and had no children. Stannis only has one daughter, who is not in great health, and isn’t likely to have more children. That means that Shireen will ultimately have to carry on the Baratheon line, assuming Stannis doesn’t sacrifice her first (Hasn’t the show done enough lately?). She is the only hope for true Baratheons… assuming Robert’s bastards don’t get legitimized, but why would anybody do that? That benefits neither Tommen, Myrcella, Stannis, or Daenerys, the only serious for the Iron Throne.

Targaryen

Yup, that’s right: House Targaryen, the deposed royal house, isn’t in such great shape either. Sure, Daenerys is going to end up being Queen of the Andals and the First Men, but Daenerys is barren. Aegon V Targaryen is probably a fake, and probably going to die at Storm’s End. Jon Snow has Targaryen blood, but he’s still a bastard, not a real Targaryen.