Hi

Your last email says "You have clarified for me that Kathleen Mary was a Graham when she married Cuthbert, not a Paton, so there is a Mr Graham to be found."

So you don't end up on the wrong track, Jogregory's email (30 April)and my earlier one both provide the reference from the NZ MARRIAGE INDEX for this marriage:

1922 TYERMAN Cuthbert Ralph to PATON Kathleen Maria

There is no 1922 listing for Kathleen under the GRAHAM surname - if she was a widow/divorced and used her married name, then both her surnames would have been indexed. She may have been divorced and resumed her maiden name - but it looks as if you won't find any details from this marriage entry.
Does Elsie's marriage entry to George Wells in 1943 show any info about her father? And does it confirm her age/birthdate (c1917) and birthplace?
Sometimes purchasing a BDM printout is the only way to get the info you need.
Best wishes with your search
Elli

P.S. Did Mary TYERMAN marry Thomas Keith CASLEY at Marrickville in 1954??