In the pokemon anime, when they say you can only have 6 pokemons on hand, do they mean like
a) 6 pokemon max you can battle with, or
b) if you're strip-searched, you can have 6 pokeballs with active pokemons on you.
Registered trainers (IE those with a dex who are competing in some sort of challenge, such as 8 Gyms and the reigonal league, or Contests+Grand Festival) are restricted to 6 Pokemon.
According to Mystery at the Lighthouse (Waay back in Kanto, something like EP014), if you have 6 Pokemon on you and catch a 7th, then that 7th is transferred back to wherever your Dex is registered. So when Ash caught Krabby, it was transferred to Professor Oak automatically. References are also made to "PC Storage" and the ability to transfer Pokemon automatically via your Pokedex.
This was never shown to happen again.
In the more recent Black White series, Ash has caught several Pokemon over the 6 limit. When he catches a 7th, that Pokemon's Pokeball becomes "locked" and it can't be used in battle until one of the other registered 6 Pokemon is rotated out at a Pokemon Center.
mind you, this question also applies to gym battle and championship league.
sometimes I wonder if there is like a government agency that prevents people from carrying too much pokemon at one time.
Gyms you simply battle (usually 3, though sometimes it's been as low as 1 and as high as 4) with whatever Pokemon you have on you. While Ash typically chooses which he'll use beforehand, most gyms don't require you to choose which 3 you'll battle with ahead of time.
In the League, you have to register the Pokemon for each battle with the League. As in, if Ash has a 3v3 battle in the League, he has to register the 3 he will use ahead of time. And he can't use anyone else during that match, even if he's carrying 6 Pokemon with him.
We've seen at least one trainer (Damien, back in Charmander's debut) who had more than 6 Pokemon on him. It's implied unregistered trainers don't have these limits that registered trainers do.
As far as governing authority, the Pokemon Center's and Gym's typically act as community centers and in some cases, even governing authorities. I know Nurse Joy has, at times, been seen as a League Inspector (see the Diamond/Pearl Special about Brock handing over his Gym Leader duties to Forrest).