The idea was that you took out the Pokemon I gave you and replaced it with said slave Pokemon...
Regardless, Shinyskarm you get Global, which can be whatever Pokemon you want it to be. Depending on its type, there's a different restriction:
Fire/Water/Grass: at the first city you reach, drop one Pokemon in the PC. Then when you get to the next city, take that Pokemon out, and drop in a different one. Wash, rinse, repeat.
Steel/Dark: You may never use fly, and you can only use 2 healing items per trainer battle. Only one of your Pokemon may use damaging moves against the Champion.
Ghost/Fighting: all your Pokemon must use held items which do not activate/have any effect in battle (so hold potions and TMs and stuff). You must also use a NVE move whenever possible with all your Pokemon.
Bug/Psychic/Ground: no using the bicycle ever, no moves on any of your Pokemon which affect the entire field (e.g. rain Dance, Trick Room, Gravity, etc.). Also two of your Pokemon must never evolve to their final forms.
The other types: you must use only 1 Pokemon to get you from Mt. Coronet to Snowpoint City, and then get you back to Eterna/Hearthome/so other city, with no healing items, though using the Pokemon Center is allowed (no switching Pokemon, though). This includes battling any and all Galactic grunts/admins/whatever's and also beating the Gym.
Regardless, these other restrictions apply. You may never utilise a TM on Global. Global must never fight in the Sunyshore Gym. Each time a Pokemon faints, throw out 1 TM and five items.
Oh, and if Global is dual-typed, then the restrictions for both types apply.