Not that there are any. This is more of a wish list.
Imagine if your Plump Turkey faced off against someone else's Ragnaros and died instantly after "Sensing his destiny." Or a Grunty and Zergling had a quick fight to the death, or took each other out right away. Two Clockwork Rocket Bots just shooting missiles at each other with no way for you to control them.
I think these little touches would be a fun treat for random PvP pet battles. Any you'd like to see?
The Curious Wolvar Pup and the Curious Oracle Hatchling, upon seeing each other across the battlefield, immediately make themselves the front pet for a battle to the death. Neither can be swapped until one has been defeated.