What would have happened to the Queen Mother's title if the Queen had pre-deceased her?

She would still have been called Queen Elizabeth the Queen Mother - the fact remains she was mother to a queen regnant. Her daughter of course always referred to her to third parties as Queen Elizabeth.

You don't stop being a mother even if you outlive your offspring - and the scenario you indicate has happened frequently in royal history. The great emphasis on the title for the late Queen Mother was because of sharing the same name as the current Queen, with no need for distintion in the circumstances you indicate, she could simply revert to Queen Elizabeth, but this would be unlikely.

The reality is she would be called what she chose to be called - Queen Mary eschewed the title of Queen Mother. Dowager Queen Mother is tautology - and the Queen Grandmother is also rather silly as she was a Great Grandmother.

Given how most people can't keep up with the Duchess of Cambridge's married name, or the Duchess of Cornwall, you have to keep things simple for the tabloid tarts to be able to keep up.

She simply would have kept her title of HM Queen Elizabeth The Queen Mother (or simply HM The Queen Mother).

She would have remained Queen Elizabeth, the Queen Mother. She CHOSE the title, herself, not wanting to be called The Dowager Queen Elizabeth; the title was not "given" to her. And the Queen Mother would ALWAYS be the mother of a monarch--one is still a parent even of the child predeceases them.

She would have remained Queen Elizabeth the Queen Mother, who would have told her otherwise.

She would be the Queen Grandmother!