Arrant means complete or absolute. Errant means (1) roving, or (2) straying from the proper course. Arrant was originally a variant of errant, but it long ago developed a meaning of its own. It has negative connotations, usually modifying negative nouns (e.g., arrant fool, arrant nonsense).
The compound noun knight-errant (always hyphenated, pluralized as knights-errant) dates from medieval literature and refers to a knight who roves the countryside engaging in adventures.
To our surprise and arrant disbelief, this is how you spend every afternoon in Ventura. [Punk News]
Sometimes I feel like the errant child who is chided to do what he is told and not ask so many questions. [Daily Advertiser]
Over the years this arrant foolishness has become a major dodge to hide what lawmakers are going to be doing … [Washington Post]
An errant pick-off throw then allowed Burrow to score and Ketler to go to second. [Massilion Independent]
This, of course, is arrant nonsense. [Swans]
The city says highway-style barricades and nets capable of stopping errant vehicles will be installed … [San Jose Mercury News]