'Jeez]' she is likely to exclaim when asked awkward questions. Her conversation is a blizzard of 'hells' and 'bloodys' and other oaths, often bawdy. She may call you a 'fuckwit' - just for a joke, of course, as she did to a colleague at a reception in 1986 when she was mayor of Auckland. Or she may embarrass you by insisting that you sing for your supper, as was the fate of Germany's president Richard von Weizsacker at a state dinner in Wellington earlier this year.
She is as likely to preside over the Weightwatchers Ball as she is an investiture at Government House, and she has admitted that a deciding factor in her becoming the Queen's representative in New Zealand and local head of state was that the job came with a pension.
Dame Cath, as she likes to be called, is perhaps best remembered abroad for her walk-on part in the American travel writer Paul Theroux's book The Happy Isles of Oceania. They met in Fiji and their rather sour encounter, which involved a coarse description of the Governor General's eating habits - shovelling food on her fork with her thumb, licking her fingers, picking scraps from her teeth and eating them - and her smugness had New Zealanders rushing with their spears to her defence.
Theroux, however, said she was a New Zealander to her fingertips: rather silly, shallow, unimaginative, bossy, vain, cunning and principled in a meddling way. New Zealanders especially didn't like that.
Whatever foreigners may say about Dame Cath, Kiwis like her. If they have any misgivings, they explain it away by saying: 'She is very down to earth, you know.' Barry Gustafason, a former university colleague and political scientist at Auckland University, said: 'She is not a foul-mouthed hard-drinking person as the (fuckwit) incident would suggest. Decency and order come to mind when I think of her.'
She may seem graceless, but her manner conceals a true professional. A senior New Zealand lawyer who has worked with her says she has 'tons of savvy, is the opposite of wimpish, not a bull-at-a-gate person, very effective and very feminine, sensitive and intelligent'. I thought he had fallen in love with her. He called Paul Theroux 'a pig'.
This week, when the final results of the country's split election are announced after counting absentee votes, she may have to lead New Zealand out of a constitutional impasse. Last weekend's poll brought a hung parliament. National, the governing party, won 49 seats in the 99-member House; it needed 51 to form a majority. The Labour opposition won 46, and two new parties, New Zealand Alliance and NZ First, collected two seats each. The final counts could change the results in some nine seats where majorities range from 10 votes to a couple of hundred.
Dame Cath will have to decide which party leader - current Prime Minister Jim Bolger or Labour Party leader Mike Moore - to ask to form a new government.
Sir David Beattie, a former Governor General and former Supreme Court judge, compared last week's vote to Britain's first 1974 general election, which left a cliff-hanger between Edward Heath and Harold Wilson.
'Heath, as the former prime minister, was asked by the Queen to form a government. He couldn't,' Sir David said. 'Harold Wilson was asked next, and he could. We haven't got to that situation yet, but in the long run the sort of government we get can only be decided on the floor of the House. I cannot see any real problem for Dame Cath as the conventions are pretty clear and she has good independent advisers.'
Born in a rural settlement in the North Island, Dame Cath progressed from a state school to Auckland University, where she met and married Bob Tizard, an aspiring Labour politician. After bearing her husband (by then an MP) four children, she won election to Auckland council on a Labour Party ticket in 1971 at the age of 40. Twelve years later, divorced from Mr Tizard, she became mayor of New Zealand's biggest city, and stayed in the job until she was appointed Governor General in 1990.
When asked what kept her going in public life, she replied: 'I've come to the conclusion it's bloody Presbyterian Calvinist doing-my-duty.'
Additional reporting by David Barber.
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