devolve (up)on (someone or something)
To become someone else's responsibility, as of a task or job. If Joe is out sick on Monday, I know that sorting the mail will devolve on me.
devolve (up)on someone or something
[for something, such as a task] to be passed on to someone or a group. (Upon is formal and less commonly used than on.) This job, I am afraid, devolves upon you and you alone. The task of repairing the damage devolved on Diane.