Accidental retains its basic notion of chance occurrence but may also imply nonessential character.
- The location is accidental and contributes nothing to the poem.
Incidental suggests a real, sometimes a designed, relationship but one which is secondary and nonessential.
- The discovery was incidental to their main research.
Adventitious implies a lack of essential relationships and may suggest casual addition or irrelevance.
- Please avoid elaborate designs with superfluous or adventitious elements.