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human
[Game of Thrones] Why are their so few Starks?

The Starks are an ancient house, possibly the oldest one in Westeros, yet they seem to have very few decedents. You would think that given that much time the last name stark would become very common in the North.  We know that the Kalstarks are an offshoot branch from long ago, but how come we never see any other cousins or 2nd cousins or 3rd cousins, or any other families with the stark name?

Why were the Starks so close to extinction?  Assuming that all of Ned's children die, who would be the heir? Would it be the Kalstarks?
gpt
Some of it is their commitment to the Night's Watch - second and third sons are as likely to join the Watch than go off to start minor houses and keep a healthy extended family.

Then you also have a run of bad luck in recent years. Ned's father was an only child, his brother Brandon died to the Mad King (along with his father), and Benjen of course joined the Night's Watch soon after the war was over.

Going back another generation, Ned's grandfather, Edwyle Stark, was an only son (and Edwyle's sister married into House Royce). Edwyle did have a half-brother by his father's first marriage, but that Brandon Stark died in childhood.

So you have to go back to Ned's Great-Great Grandfather to actually get to extended family. Beron Stark had five sons; Donnor died without issue, William was Ned's Great-Grandfather, Artos had two sons, Errold didn't marry or have kids that we know of, and Rodrick had two daughters (one of whom was actually Ned's mother as well).

So sadly the seed has not being strong with the Stark's the last few generations. Should all of Ned's children die, Artos's branch of the family would likely have the strongest claim (Artos being Ned's Great-Great-Uncle). His two children are known to have issue, but we don't know where they ended up (or if any of them were sons).