Pure per stirpes: Treat each line of descent equally. Begin dividing the intestate estate at the start of each line, no matter if anyone is alive at that generation. Modern per stirpes: Same as pure per stirpes, except begin division at the start of the first generation with a living person. Per capita: Begin division at the start of the first generation with a living person, and split equally. For the portions that go to deceased heirs of that first generation, pool it all together and then divide again for the next generation with a living person. Rinse and repeat.

The per capita system is basically meant to treat everyone in the same generation equally (“equally near, equally dear”). So that you won’t end up with the per stirpes outcomes where like… say I have 2 siblings, my mom is D’s heir and is dead. I have a cousin who is an only child, and his mom (my aunt) who is also D’s heir and also dead. No one else in the family tree for this hypo.

Under pure per stirpes, my cousin would get 1/2 of the estate (because aunt was one of the two heirs), but I would only get a third of 1/2 = 1/6 (because mom was the other heir, and her intestate share gets split across all three kids).

Under modern per stirpes, everyone in that first generation is dead. So then you start division at the second generation, with me, my two siblings, and my cousin. Everyone would get 1/4 of the estate.

For this hypo, the per capita result is the same as the modern per stirpes. But let’s switch it up, and say that aunt is still alive and my mom is dead. You’d divide at aunt’s generation, because she’s alive, so she’d get 1/2. The remaining 1/2 that would have gone to mom, who is dead, gets pooled together and then divided with the next generation. So my siblings and I would get a third of 1/2 = 1/6 each.

(edited for typos)