Hi Ferd II,
I have partial success, based on your advice and suggestions and a (new) understanding that the iCloud Calendar data is the "master" data.
I first confirmed that the iCloud data was correct and did not include any subscribed calendars. On the Mac I went to System Preferences > iCloud and turned off Calendar, electing to delete calendar data from the Mac. I then went to Settings > iCloud on the iPad and again turned off Calendar, electing to delete calendar data. I then repeated that exercise on the iPhone. This returned all calendar installations to the new default settings (i.e. one calendar named Calendar.)
However, a single subscribed calendar appeared on the iPhone ONLY, and all attempts to remove it failed -- the Delete Calendar function simply doesn't exist. The only available option was to choose its colour. Note that this is a valid subscription and continues to work properly despite the problems surrounding it.
I then visited each device in turn and reestablished the Calendar ON option in each of the iCloud areas -- System Prefs > iCloud on the Mac and Settings > iCloud on the iPad and iPhone. I'm very pleased to adivise that the problem of duplicated events has now disappeared, thus my original question is answered.
The question of the subscribed calendar remains. This calendar appears on the iPhone ONLY -- not in iCloud, not on the iPad, and not on the Mac. Since this appears to be an aberration I would like to delte that calendar and resubscribe anew. But, I can't find any way to delete it, or any instructions in iCloud Help about subscribing to a calendar that someone else has published. I wonder if you are able to make any suggestions ?
Many thanks for your help so far.
Steve.