A propósito vs. adrede vs. intencionalmente

The words 'a propósito', 'adrede', and 'intencionalmente' in Spanish all translate to 'intentionally' or 'on purpose' in English. However, they are used in different contexts and have slightly different connotations.

A propósito

'A propósito' can mean 'intentionally', but it is often used to mean 'by the way' or 'incidentally'. It can also refer to something being relevant or pertinent.
A propósito, ¿has visto a Juan hoy?
(By the way, have you seen Juan today?)
Hiciste eso a propósito para molestarme.
(You did that on purpose to annoy me.)
Tu comentario es a propósito para la discusión.
(Your comment is pertinent to the discussion.)

Adrede

'Adrede' strictly means doing something intentionally or on purpose, usually with a negative nuance. It often implies that the act was committed with malice or harmful intent.
Rompiste mi vaso adrede.
(You broke my glass on purpose.)
No lo hizo adrede, fue un accidente.
(He didn't do it on purpose, it was an accident.)

Intencionalmente

'Intencionalmente' translates directly as 'intentionally'. It is often used in formal contexts or when referring to deliberate actions or thought processes.
Fue despedido por actuar intencionalmente contra las políticas de la empresa.
(He was fired for intentionally acting against the company's policies.)
La jugadora intencionalmente cometió una falta para detener el juego.
(The player intentionally committed a foul to stop the game.)

Summary

'A propósito', 'adrede', and 'intencionalmente' can all be used to convey the idea of doing something intentionally or on purpose in Spanish. However, 'a propósito' is more versatile and can also be used to express pertinence or to transition into another topic ('by the way'). 'Adrede' typically implies intentionality with a negative connotation. Lastly, 'intencionalmente' is more formal and often refers to deliberate thought processes.