As an adjective it implies a pertinance to the author of Alice's Adventures in Wonderland. The noun form (Carrol)is far more formalized, used only in instances where the subject is quite familier.
1: Used to describe someone who uses nonsensical words with relative ease.
2: A person who is capable of saying a silly or ridiculous sounding word or phrase without actually sounding ridiculous.
3: Someone who routinely replaces actual words with words like 'flibbertygibbet' or 'whatchamahoozit' yet somehow manages to convey the meaning of the intended word.
John recited the Jabborwocky for us in class today. He is surprisingly Carrollian.
A woodland creature the size of an antelope but much smaller. Covered from head to toe in shag carpeting, it is capable of moving at speeds of over two miles per hour. Over time it has evolved the hind legs of a steam shovel. A timid creature, it is rarely seen during the day. At night it ventures forth, using its long proboscis to seek out nourishment. It feeds exclusively on honey.
Me and Jimbo went'a Vagina huntin' the other day...