What is a word for when you pass the responsibility of something to someone or something else?

e.g. I x my responsibility of self-defence to the state.

Solution 1:

cede (sēd) TFD

To surrender possession of, especially by treaty. See Synonyms at relinquish. To yield; grant:

As in:

I cede my responsibility of self-defence to the state.

Solution 2:

Delegate: verb (with object) entrust (a task or responsibility) to another person, typically one who is less senior than oneself.

• She must delegate duties so as to free herself for more important tasks.

• The power delegated to him must never be misused.

• I delegate my responsibility of self-defence to the state.