Mike Tyson probably, and Lennox Lewis. But after him the grandeur seemed to disintegrate into a succession of non-entities contesting three, four, or is it now five different titles?
If Duco Events can find enough corporate sponsorship next week to stage the fight in New Zealand, it would be wonderful. But the corporates will not be investing for international exposure, the domestic audience would be their reward. And it would be considerable.
Parker is an appealing man, refreshingly normal and Kiwi modest. We are going to be with him whether his big fight is here or in the United States. In some ways, it will be better if he has to go over there and prove he can do it. For we don't yet know how good he is.
We get equivocal assessments from serious fight followers such as Sir Robert Jones. Possibly even those closest to him, and he himself, doesn't know how good he is yet. He has beaten everyone his handlers have brought here and put in front of him, but so had David Tua until he got a shot at a title and what an anticlimax that proved to be.
It was hard to watch Tua flailing hopelessly at Lennox Lewis without feeling like we, the New Zealand public, had been played for fools. We hadn't been asked for money, fortunately, but we'd been fed an excessive dose of hope.
Public money and professional sport are not a good mix. Look at the America's Cup.
Watching Duco and Kevin Barry promote Parker's previous fights, I've tried to resist cynicism. Because the cynicism I hear on any subject I understand, it is just about always wrong. I don't know anything about boxing, as a sport or show-business, but it appears that boxers on their way up are carefully kept unbeaten for the sake of one really big pay-day.
The sport would have more credibility for me if somebody at Parker's stage had suffered a loss or two along the way. Everyone in every sport will have an off day. That is sometimes when their class becomes most apparent.
Lydia Ko had a couple of bad days at the Olympic Games and even in that final round her birdie putts were not going down. But they way she kept her cool, stayed in touch and charged on the final few holes to take silver, was the mark of a champion.
Ko would make it well worth investing public money to establish a top-class women's golf tournament here that would showcase our landscape and attract tourism in a way that boxing cannot. But I rather hope that doesn't happen either. Public money and professional sport are not a good mix. Look at the America's Cup. Team NZ has never won it since the Clark Government put money in.
John Key's Government has maintained the investment but I don't think he rates it highly. He has been noticeably not anxious to attend the America's Cup, even when we were on the verge of regaining it at San Francisco.
I think we've all given up the idea that our public money is in the America's Cup to showcase the country. It is there for the sheer pleasure it gives us, or most of us, every four years. In between times it's a wretched business of promotional hype and contrived competitions but when the real racing starts, I'm enthralled.
So it will be when our boy climbs into the ring in Dallas or wherever in the US it might be. He will be going where Scott Dixon, Steve Adams and Lydia Ko have gone to give us glory, even if we are the only ones watching.