Used when someone gets a duty because another person can't or won't do it anymore. When the manager retired, her tasks devolved on the assistant.
Pro Tip 2/3
Often Formal
Commonly found in legal, business or formal texts, rather than casual conversation. The role of chairman devolves on her in the event of the president's absence.
Pro Tip 3/3
Reluctant Acceptance
Can imply taking on a responsibility unwillingly or by default. The burden of proof has devolved on the accused party.