Hand over the baton verb phrase
The phrase denotes a relay race where a runner passes the baton to the following runner. The verb "pass" can substitute for "hand over" in the phrase. If the verb "hand over" is replaced by "pick up", the phrase means that somebody accepts a particular duty or responsibility
To give someone a particular responsibility or duty
He must be a trustworthy and qualified person, so his father handed over the baton to him when retiring.
You should find a responsible person to hand over the baton.
Being looked after or protected by someone
It is used to tell someone that it is time for them to take action or make a decision.
If something falls (squarely) on someone’s shoulders, it is the responsibility that one have to take.
Used to indicate the responsibility belongs to someone, normally a negative one.
The verb “hand over” should be conjugated according to its tense.
The baton passed from hand to hand in a relay race is first mentioned by that name in 1921. This use gives rise to “pass on the baton”, to hand over a particular duty or responsibility.