Usually you can release five copies of the same Pokemon at the Release Kiosk to get a ticket for a Pokemon from the evolution line of the released Pokemon. You can obtain special tickets by releasing the following combinations of Pokemon.

Ticket	How to unlock
Articuno	Pidgeot, Fearow, Jynx, and Lapras
Burmy Sand/Trash Cloak	Five Mothims
Cut Rotom	Rotom and Leafeon
Darkrai	Wash Rotom, Heat Rotom, Spin Rotom, Cut Rotom, and Frost Rotom
Dialga	Dragonite, Bastiodon, Lucario, Garchomp, and Magnezone
Frost Rotom	Rotom and Glaceon
Gastrodon West Sea	Five Shellos East Seas
Giratina	Gengar, Dragonite, Garchomp, Spiritomb, and Dusknoir
Heat Rotom	Rotom and Flareon
Manaphy	Three Phiones
Mewtwo	Dialga, Palkia, and Giratina
Moltres	Charizard, Pidgeot, Fearow, and Magmar
Palkia	Blastoise, Gyarados, Dragonite, Empoleon, and Garchomp
Phione	Lapras and Vaporeon
Shaymin	Arcanine, Charizard, Kangaskhan, Bastiodon, and Arbok
Shellos West Sea	Five Gastrodon East Seas
Spin Rotom	Rotom and Jolteon
Wash Rotom	Rotom and Vaporeon
Wormadam Sand/Trash Cloak	Five Burmy Grass Cloaks
Zapdos	Pidgeot, Fearow, Raichu, and Electabuzz