While I’d heard of this or that giant vegetable winning awards at fairs I’d never really paid a whole lot of attention. But while I wasn’t watching giant vegetable growing has become a serious competitive sport. I expect much of that has to do with the internet allowing far flung devotes to connect.
If you are looking to connect with other giant vegetable growers you might start with Giant vegetables at the Garden Web Forum
Growing giant vegetables is much like growing giant flowers.
1) Start with a good variety, heirloom is best.
2) Remove all other fruits or flowers so all the plants energy into the one you want to grow supersized.
3) Fertilize regularly
4) Water regularly
5) And a bit of luck is need.