Four seasons in, Game of Thrones is littered with the corpses of dead patriarchs from great families: Robert Baratheon, Ned Stark, and now Tywin Lannister. Their wives and mistresses haven't fared much better. Game of Thrones has become notorious for its willingness to kill off major characters, but the weekly discussions of "shocking" deaths sometimes overshadow the far more interesting question the series is asking: What effects do those deaths have on the people left behind?

Last night's season finale, "The Children," tackles the futures of those great houses without the men who once served as their leaders. In every case, their children have been left to carry on their legacies after their deaths. And in every case, their children have branched from the paths their parents would have chosen for them.

Though he's been dead for most of the season, the specter of Joffrey Baratheon has loomed heavily over Game of Thrones this year. In a key scene during Game of Thrones' second season, Tyrion still believed there was a chance to turn Joffrey around before he descended into full-blown sadism. "Do you think I haven't tried?" said Cersei. "He doesn't listen to me. Sometimes I wonder if this is the price for what we've done. For our sins."

But for all the pathos of Cersei's desperate lament, "The Children" makes it clear that Cersei was wrong. You can talk about history and lineage, parenting and birthright, but parents can't control what their children do. Just as Cersei wasn't directly responsible for every act of evil committed by Joffrey, she can't be credited for the inherent goodness of Tommen, the gentle son who took the throne in Joffrey's stead.

That uncomfortable uncertainty doesn't just apply to the incest-born children of the Lannisters. (Even Daenerys, the mother of dragons, finds that her "children" are suddenly beyond her control.) In theory, anyone, regardless of birth or opportunity, could turn out as sadistic as Ramsay Bolton or as noble as Jon Snow. The latter plays a key role in "The Children," recovering after last week's vicious battle with the wildlings — and when Stannis Baratheon shows up with some much-needed reinforcements, he asks Jon Snow what Ned Stark might have done with Mance Rayder. "I think my father would have taken him prisoner," says Jon. "Listened to what he had to say."

It's the right answer, but I'm not convinced it's the one Ned Stark would actually have given. Three years ago, Game of Thrones began as Ned Stark beheaded a deserter from the Night's Watch — a man who warned about the approach of the White Walkers long before they were on anyone else's radar. Given a similar opportunity in "The Children," Jon Snow shows more mercy and more strategy with Mance and his wildling army than Ned Stark's black-and-white worldview would ever have allowed.

It's also the only merciful moment in "The Children," which is otherwise devoted to children striking back at their fathers with a little more bite. Cersei, caught between generations (and lacking the power to influence either), stabs at Tywin with the sharpest weapon in her arsenal: The truth about her long affair with Jaime. "How can someone so consumed by the idea of his family have any conception of what his actual family is doing?" she marvels. "One real look at your children and you would have known. Everything they say is true about Jaime and me. Your legacy is a lie."

It's the first in a series of betrayals by Tywin's children that eventually culminate in his death. Tyrion may deliver the kill shot, but it's Jaime — however unknowingly — who gives him the opportunity to do it. And it happens shortly after a scene in which Jaime once again leafs through the book detailing all the great, heroic deeds of the Kingsguard, stopping on his own conspicuously empty page.

"I would do things for my family you couldn't imagine," says Cersei later in the episode, and it's clear that she means it. But for all the ways Tywin has belittled, mistreated, and manipulated Cersei and Jaime — and for all their efforts to escape his grasp — they're still stuck in the world he created for them. Cersei's son is on the throne because of a political marriage that Tywin arranged, and Tywin's death won't mean the end of Tommen's reign. Jaime's service in the Kingsguard is supposed to be for life, but given recent circumstances (and Tommen's ability to dismiss him from his duties), that may not last; Tywin will need someone to serve as his heir.

At first, it seems that Tyrion might have escaped his father's grasp, after a series of developments so perverse that they give Oedipus a run for his money. First, Tyrion discovers Shae in his father's bed and strangles her to death. Next, he discovers Tywin on the toilet, and Tywin admits that he's always wished Tyrion was dead. "But you refused to die," says Tywin. "I respect that. Even admire it."

It's the same kind of speech we've heard Tywin unleash, successfully, on all three of his children many times before, and he clearly thinks it will work again. But Tyrion has had enough of his father's cruelty, and of pining for the birthright he's always been denied. He shoots Tywin with a crossbow, allowing his father one last pointed barb: "You're no son of mine." But for once, Tyrion gets the last word: "I am your son. I have always been your son."

Given his father's legendary ruthlessness, those words have never been more accurate — but they also mark the end of Tyrion's claim to the proud Lannister legacy his father worked so hard to build. "The Rains of Castamere" will soon fall out of fashion, and a new song will have to be written: A song about a vengeful imp who killed his own father while he was sitting on the toilet. But though the events of "The Children" will likely dismantle some of the legacy Tywin worked so hard to built, they also prove Tyrion to be the truest member of his family after all: What is a Lannister if he doesn't pay his debts?

Tyrion won't be around to see the immediate aftershocks of his actions; Varys smuggles him to the safety of a departing ship before he can be captured. It's a moment that sets up an unexpected and intriguing parallel with another character whose life has been defined by her birth into a storied Westerosi family: Arya Stark.

Arya has always been one of Game of Thrones' most strong-willed characters, but the series has spent much time buffeting her around due to events beyond her control. She was brought to King's Landing by her father, then forced to flee after he was executed. In the seasons since, she's been marched around Westeros by everyone from Yoren of the Night's Watch to Tywin Lannister to The Hound. Arya has never had control of her fate — and when Brienne of Tarth appears in "The Children" to offer yet another dubious form of protection, Arya turns her down flat.

The Hound loses his subsequent battle with Brienne, and like Jon Snow, Arya has the chance to make the kind of choice that once belonged to her father: Should she seek mercy, justice, or vengeance? The Hound has served as her protector, but his name is also on her list, and he doesn't shy away from the crimes he has committed.

In the end (and despite his pleading), she chooses not to kill The Hound — an act of cruelty that doubles, paradoxically, as a kind of mercy. But regardless of the outcome, the true importance of her decision is her refusal to be influenced by his threats, his insults, or his pleas. For all her inner strength, Arya has always been a pawn in the game of thrones — and while Cersei once said the only options are "win" or "die," Arya has embraced her newfound agency by discovering a third option: Removing herself from the board altogether. As "The Children" ends, she sails off to a strange new place, hundreds of miles away from anyone who will ever be able to recognize her as Arya Stark. Her name and her birthplace are long gone, and her legacy is no longer secure — but for the first time, there's no question that she's the one who will get to define it.

Read more Game of Thrones recaps: