Coniglio bianco appears solely in the Alice in Wonderland episode (episode 14) of the anthology series, adhering closely to Lewis Carroll's original narrative. As the catalyst for Alice's journey, he first captures her attention through visible distress about tardiness, then lures her into Wonderland via the rabbit hole. His defining trait remains an obsessive focus on punctuality and schedules, marked by repeated anxiety over a critical but unspecified appointment. This fixation solidifies his role as a herald figure, driven by time-bound duties likely tied to the Queen of Hearts.

Within Wonderland, he engages with Carroll's iconic characters, including the Cheshire Cat and the Queen of Hearts. A pivotal incident involves his mistaken identity of Alice as his housemaid Mary Ann, where he assigns her domestic chores. This error traps Alice in his dwelling after she consumes size-altering substances.

The character resurfaces in the episode's conclusion, performing formal herald duties during the King and Queen of Hearts' proceedings, cementing his position within Wonderland's royal hierarchy. The portrayal aligns strictly with Carroll's source material, emphasizing his plot function and perpetual traits of haste and nervousness throughout the standalone episode.