On a weird footnote to my previous post; under the present constitution of Australia if Charles ceased to be King of England for some reason he would still be King of Australia and as such could move to Australia and take over the constitutional duties of the Governor General, who is, in effect, his proxy in Australia.
I believe the same probably applies to Canada and about 12 other Commonwealth countries; Antigua and Barbuda, Bahamas, Belize, Grenada, Jamaica, New Zealand, Papua New Guinea, Saint Kitts and Nevis, Saint Lucia, Saint Vincent and the Grenadines, Solomon Islands, Tuvalu