を〜に任せる means "to leave something to someone": you hand over a task or a decision and let them handle it their way. The task takes – or when it is the topic – and the person it goes to takes .
。
I'll leave this work to Tanaka.
。
I leave the cooking to my mother.
。
I'll leave the decision up to you.
The person never takes を; that slot belongs to the task.
任せて and 任される
on its own, with
or without, is the everyday "leave it to me". The passive
is the other side: you are the one entrusted, and the task still takes を.
、。
Don't worry, leave it to me.
。
I was put in charge of a new project.
任せる or 頼む
asks someone to do a particular thing. 任せる hands over the whole matter, including how it gets done, and implies you trust them with it.
。
I asked Tanaka to make copies.
。
I left the meeting preparations to Tanaka.
Leaving things to chance
With , or , you stop trying to control what happens. It often carries some resignation.
。
We have no choice but to leave the result up to luck.
。
I intend to leave everything to take its natural course.
before another verb means acting on an impulse rather than thinking:
, "in a fit of anger".
、。
I said something terrible in a fit of anger.