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helenS two ways I believe under our loose and largely unwritten constitution.
First she could abdicate (essentially renounce her throne). Exactly as her uncle Edward VIII did in 1936. However I think the memories of that run deep in her majesty. It put her unprepared father on the throne through WW2 and arguably shortened his life with the stress etc of suddenly being monarch. Also it made her heir apparent overnight.
Her fervent belief is the job is for life and you have duties as monarch or an hier. See how she stripped Harry of title and privilege. If you don't work then you're outcast in her view.
So I feel it highly unlikely she'll abdicate.
Secondly a regency. That is when someone rules in place of a living monarch who can't. Examples in history are when young princes came to the throne before age of maturity. But they are clouded in scandal.... Richard III for example.
Closer example to today's situation is George III who whilst a long reigning monarch was incapacitated through some mental illness for many years, either porphyria or bipolar (scholars argue that). In that case his Queen and the Prince of Wales acted as monarch under a regency act passed through Parliament.
A regency where Charles becomes Prince Regent in the Queen's place would be to me more likely. At the jubilee he took the salute at the trooping the colour, he recently read the queen's speech at the state opening of Parliament. So in some ways he is already doing this but Queen still deals with the weekly audience with the pm and signing all legislation etc. If she couldn't do that that is when a regency would be enacted I think and Charles would take over all duties.