Question

What factors are most likely to influence whether the star eventually ends up as a neutron star or as a black hole?

Answer 1

Mass

Explanation:

There is only one factor that determines if a star will turn into a white dwarf, neutron star or black hole after it's "death" and that is it's mass. The reason for this is it is gravity.

If the star remnant has enough mass and therefore gravity to squeeze together all the subatomic particles so that there is no space between protons and electrons, then you have a white dwarf. If the star has enough gravity to fuse protons and electrons together to form neutrons (the whole star will not be neutrons but a large amount will be) then you get a neutron star.

If the star remnant is large enough that the force of it's gravity actually cause neutrons to fuse together until all you have left is a super high mass singularity, then you have a black hole.

We know roughly what mass is required for each as well, and we relate it to the size of our own star then sun. A star roughly half the size of our sun to about 10 times the size of our sun will form a white dwarf. 10 times to 29 times the size of our sun forms a neutron star. Larger than that forms a black hole.