Changes to animal companions:
1: At first level animal companions get full hit points possible for their hit dice (just like player characters).
2: The next time the animal companion gains hit dice the player may choose to have the animal companion gain the normal 2/3rds possible hit points or roll the hit die. Once this choice is made it cannot be changed.
Notes for animal companions and familiars:
1: Make a character sheet for animal companions and familiars here on Obsidian Portal along with the one for your character.