Mass of black holes compared to parent star What is the range of percentage mass of parent star left in a stellar black hole directly after its formation?

What factors determine this number for a specific case?
There is no general consensus on this. Different evolutionary models give different results. The factors (in addition to the initial mass of the star) that effect the final black hole mass would be the rotation rate of the progenitor, its composition (or metallicity) and whether it was in a binary system or not and whether that binary system was able to transfer mass.

Rotation is thought to be important because it affects internal mixing and therefore the rate at which fuel is supplied to the core and the rat at which processed material gets to the surface, affecting the atmospheric composition. It can also enhance mass loss.

The composition is important because mass loss is driven by radiation and radiative opacities are higher for high metallicity compositions.

A set of calculations by Heger et al. (2003) are one of the canonical works on this subject. Below is a plot of initial mass versus remnant mass for stars with big bang primordial abundance (zero initial metallicity) and then the same again for stars of solar metallicity. 

The ratio of the red line to dotted "no mass loss" line gives the fraction you are after. 
In zero metallicity (primordial) stars it increases from 10-40% for initial masses of 25-100 solar masses and is perhaps even higher for supermassive population III stars. (I stress that these are theoretical results).

For solar metallicity stars the results are a bit different. The ratio of the red line to the dotted line varies from 10-25% for 25-40 solar masses, but then it is not clear whether black holes can even form at even higher masses because of the much higher mass loss rates (see the difference between the dotted line and the blue curve).