It depends, but thanks to the Noble Houses constantly intermingling amongst one another, we'll likely be able to trace the ancestry back far enough to produce an heir, hopefully.
In Westeros, they follow the Primogeniture rules of succession; which means that the Heir must be a legitimate male, until such time as all of the prime legitimate males are deceased, at which point, it goes to the eldest female. But if none are found, then it goes to the subject's next male heir (brother, cousin etc), and the process is repeated until a suitable candidate is found.
There is an issue of difference between the books and the TV-show. In the show Game of Thrones, bastards are not permitted to inherit anything under any circumstances! (unless they are legitimised by Royal Decree).
Whereas in the books, A Song of Ice and Fire, bastards are allowed to inherit, "if the father has no other trueborn children nor any other likely kin to follow him."@.
This may cause some slight complications in our calculations, so I will separate the results below.
- Let's assume Stannis is deceased, and his issue also all deceased
- Robert is deceased, his issue are either baseborn (illegitimate) or not even his (Joffrey, Myrcella, Tommen)
- Renly is deceased, without issue
Let's follow the white rabbit:
There is no possibility of jumping the lineage to a married branch of a house, if that were the case, then Stannis' successorship would go to Selyse Baratheon nee Florent's family; who's lineage is another clusterf#@$ ending in Melessa Tarly nee Florent (Sam Tarly's mother, so Sam's brother Dickon would be Stannis' heir, lol). So no help there. We have to go further up the tree.
Stannis had a father, Steffon Baratheon. Steffon didn't seem to have any siblings, and all of his children are deceased without heirs (we're also skipping his wife, as above), so let's go further.
Steffon's father, Ormund Baratheon seemed to have a sister; she was unnamed but was originally betrothed to Prince Duncan Targaryen (Duncan The Small). Duncan broke off the betrothal when he fell in love with Jenny of Oldstones. This is what caused King Aegon V Targaryen to marry off his daughter Rhaelle to Ormund Baratheon. There is no other detail on this unnamed sister, but her children would have been next in-line if they were included!
We could go even further back though, Lyonel The Laughing Storm Baratheon, who was Ormund's father, but again Lyonel seemed to be an only child.
It's getting quite sparse, and at this point it is worthless to dig any further back as the only other person we have information on is Orys Baratheon (the first Stormlord and first Hand of the King), but the line seems to whittle down to single children#, and there would probably not be any living descendants or "likely kin to follow", leading us back to Lyonel Baratheon, etc.
Let's come back down to earth and dig a little bit closer to home. Robert had many baseborn children, a few of which were acknowledged by him, including Edric Storm and Mya Stone. Mya is the eldest of his bastards, Gendry is the eldest male but Edric is the eldest acknowledged male (and is also the most lordly, having been grown up at Storm's End under the care of Ser Cortnay Penrose.
- If these bastards are allowed to be in line, then they can probably continue the Baratheon lineage nicely, given that they are all such strong embodiments of Robert's characteristics and the "Baratheon look".
If it were up to me, I'd go with Edric Storm (being that he is the most lordly), but it could easily go to our favourite bastard, Gendry The Bull!
- Stannis - deceased and so are his issue
- Robert - deceased without legitimate issue
- Renly - deceased without issue
So the problem here is that there's no history past Stannis' parents (Steffon Baratheon and Cassana Baratheon nee Estermont), so there's no guarantee who their ancestors were. But the only thing we do know for sure is that they had a Targaryen great-grandmother, Rhaelle Baratheon nee Targaryen (this is the same as the books). Unfortunately though, this doesn't help us, as the succession doesn't jump to someone who married into the family.
The only hope at this point, is:
- Option 1: to do a depth-first search into the family tree, and find a child or sibling from either Steffon Baratheon (Stannis' father), Ormund Baratheon (Stannis' grandfather), Lyonel Baratheon (Stannis' great-grandfather) or all the way back to Orys Baratheon (the first Stormlord).
- Option 2: Legitimise one of the bastard sons of Robert - most likely, Gendry (given that in the show, Edric "Ned" Storm doesn't exist).
So there you have it, when it truly comes down to it, the only hope we have for the Baratheon lineage is for one of Robert's bastards to pick up the mantle!
@ Pay attention to this, it will be important for us here.
# There are several families which we can follow, but none seem relevant at this point, these include: