Hi, I have been curious about this for a while. My father died of natural cause during my transit Pluto square sun transit (3 degrees separating).
That's called "coincidence." It is not Astrology, not to mention that Pluto is way out of orb for a transit (orbs are 30' of arc). The Planet Pluto does not represent death and never did.
I've heard that Pluto transits to Sun or Moon in the child's chart could be indicative of the natural death of a parent.
That's bad astrology. I had transiting Pluto square Natal Sun, oppose Natal Moon, oppose Natal Mars, square Natal Uranus, square Natal Pluto, oppose Natal Sun and then square Natal Moon in that order. Nothing happened.
I will live to see transiting Pluto oppose Natal Pluto, conjunct Natal Moon and beyond.
I've also posted quite a few charts for dead people, and transiting Pluto was never a factor in any of the charts. Some of those charts were suicides and there was no Natal Sun/Pluto conjunction which destroys that myth (see the stupid thread in the "Psychology" section with the very bad book written by a very poor Modern Astrologer needlessly frightening people out of their wits), but then common sense should prevail, because any Planet conjunct the Sun is Combust and effectively powerless (unless it happens to be Cazimi).
I agree with Robert Schmidt in that you need about 200 charts to have a theory considered.
Just glancing at Prince Henry's chart, transiting Pluto was inconjunct Natal Moon by Sign (not to mention out of orb by 19°) and 20° out of orb with Natal Sun. In fact, transiting Pluto makes no aspects whatsoever to natal Planets in his chart on the day his mother (Princess Diana) died.
Looking at Prince William's chart, once again, nary an aspect by transiting Pluto. It has separated from Natal Uranus by 1°, but then it would be totally absurd to suggest that transiting Pluto conjunct Natal Uranus heralded the death of his mother. That would be really really bad astrology.
Even in Diana's chart, there are no aspects although transiting Pluto has separated from a square with Natal Mars by more than 1°. Given their Sign placements and House rulerships, suggesting that transiting Pluto square Mars portended the death of Diana is huge leap.