Super simple question, but I can't find the answer on the Internet (and I'm in a foreign country so the library is not English.) As the title says, what is the smallest scale at which blood vessels, nerves, lymphatic vessels, bronchi, renal structures, etc.. are deterministic (same for most of the population)? For example, I'd imagine capillaries are pretty much random, while (most?) people have an aorta, so where does the pattern break? Is there a scale at which an animal's body is probably similar to their siblings but dissimilar to a complete stranger? Or is it just a statistical distribution thing (the smaller you go the more standard deviation you get)?
Indeed a very good question. I'm afraid it might remain without a proper anatomy-based answer, but my intuition would tend towards agreeing with "the smaller you get, the more deviation you'll find".
Or rather, I would expect the same principle as in conservation of genetic patterns to apply here: the more central a tissue structure is to survival, i.e. the more downstream systems depend on it, the more likely it will grow in conserved patterns.
As an excellent example, the largest blood vessels including the aorta and its first- and second-degree branches are identical in branch number, approximate relative branch size and approximate branching location across probably all living humans (given that babies born with malformations on this scale would probably not survive without drastic surgery). Similarly, the largest-level nerves and nuclei are identical across the species. These are central systems that provide core functionality for survival.
On the other hand, teeth are quite important, but the odd tooth missing or additional doesn't harm terribly as no downstream systems depend on them. Indeed, it isn't uncommon for humans to be missing a permanent tooth and keep their primary (baby) tooth in that spot for decades; similarly, missing 8th teeth or additional 9th teeth also occur.
The answer is... basically none. The variability is high, and can also happen in the macroscopic range. If you want a quick-and-dirty idea of the fraction of the population presenting a certain variability in humans, I would suggest a good anatomy atlas or manual. A good resource would be Gray's Anatomy (the book, not the soap ;-).
Apart from that, @Armatus is in my opinion correct in assuming that variability is inversely proportional to scale. However I would like to point out that even the largest blood vessels can derive from the classical structure in many ways, and are certainly not identical among all living humans.
Biology is not deterministic. Traits like this have variable expressivity.
A phenotype with 100% expression in a population with an allele is said to have complete penetrance. There is no gene which could specify a single blood vessel pattern that could have complete penetrance. Variable expressivity means the same genes yield a spectrum of forms of the same phenotype.