Simmental I'm the most familiar with. You can register and show 1/2 Bloods and 3/4 Bloods as percentage Simmentals. A 7/8 Heifer is considered Purebred and a male is at 15/16. We ran a mostly purebred operation starting from my Grandfather's Angus herd.
Chianina allows any percentage to be registered. They also have "two " breeds. Chiangus must only be Chianina and Angus crosses only. Chianina (and Chimaine) can be any cross of breeds with a percentage being Chianina. Commercial cows are "registered" and given a Commercial number. The breed of those cows is also recorded. Because of problems in the past, sometime DNA results may be required. Percentages don't matter except with any National Show, Sale or Association Event. Then, they must be a minimum of 6.25%. That number may increase with time but with all the clubby bulls that were being used on commercial herds, things got away from them.
The Maine Anjou breed has 3 categories to show in with your up breeding. But they have Fullblood, High Percentage (75% and up) and Mainetainers (25% to 62.5%).
Limousin allows for up breeding. They have the Limflex which are their lower percentage and then their purebreds. I believe it's the similar to that of the Simmental.
Charolais has their Purebreds (or Fullblood) and now registers Composite Charolais, cattle crossed with Charolais. I do not know the requirements of that breed.
Those would be you more common i.e. popular breeds. The best source of information would be the respective breed associations. Call them. Jot down some questions first and call. that's what they're there for...
Hope that gives you a little direction...