How far apart do scientists estimate was/were the dying star(s) that supplied th

Question

How far apart do scientists estimate was/were the dying star(s) that supplied the elements that comprise our sun, planet, and us? With stars so far apart and expansion of space (as I understand it) carrying things further away still, it would seem to be a low probability occurrence for sufficient quantities of elements blown out from across many light years to accumulate to birth a star system.

And another related question, it would seem that when a star went supernova and blew heavier elements in all directions, that would result in mass densities for future star nurseries far away from the dead parent that were much lower than what the parent had, so won't favorable conditions for star births monotonically decrease?

Explanation / Answer

What follows in not a very good answer. In fact it is just a few random facts that may change your understanding of the overall picture.

I'm rather hoping that bumping this question on the active queue will attract the attention of someone much more knowledgeable than I am and get us a good answer.

Most of space--the intergalactic voids--is indeed very, very empty and stars essentially do not form there.

Matter in galaxies is bound in a deep gravitational potential so that it is not--for the most part--spreading out on that scale.

The loose gas and dust in galaxies is neither uniformly distributed nor static. It is acted upon by light pressure and gravity and is full of shock waves of varying densities and strengths from several stages of the evolution of stars. Moreover there is a great deal of it at any given time.

Where high density local fluctuation exist they may---subject to angular momentum limits and other constrains--compress under their own gravitation to become more dense.

Stars lose matter into interstellar space by at least two mechanism:

Late in their life cycle many main sequence stars blow off shells of gas as they expand into red giant phases. High mass stars they can do this over and over again generating multiple solar masses of ejected dust. These generate very gentle, low density shock waves.

Supernovae eject significant fraction of the progenitor's mass. These can generate powerful, high density shockwaves which overtake the mass-loss shells.

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