Hi Jack. Before I read your latest response I fixed my problem (phew!). After repeated attempts to log in in recovery mode I suddenly got it. When I went into disk utilities I noticed there were three partitions on my hard disk - HD, HD-data and another HD-data. I can only guess that that happened during my attempts to migrate data from my old Mac Air. Anyway - I erased everything from those 'partitions' and then I was able to reload the Mac OS - successfully - and I set up my iMac . The only frustration I now have is that not all of the applications on my old Mac Air can be transferred to my iMac - in particular Microsoft Word and Microsoft Excel. I am resigned to having to purchase new copies that are compatible with my "Catalina" OS. The only other odd thing is that one of my folders on my Mac Air (containing some video files will also not migrate) but I have loaded this into my iMac manually. Anyway - "happy days" now. Thanks for sparing your time to look at my problem. Stay safe and keep well!