>>45031784The only Pokemon medium where there is no limit of six is the manga.
In the games, you can only carry six Pokemon.
In the anime, if you catch another Pokemon while you already have six with you, the Poke Ball either teleports away to the Professor's Lab (the original series), or remains locked until you remove another Pokemon from your party (BW).
In the manga, you're allowed to have as many Pokemon as you can physically carry, but 6 is the maximum amount that are allowed to be used in official battles and is also stated by Oak to be the maximum amount at which a trainer can give all of them sufficient care and attention.