contribute means "to give" it has an underlying meaning that you and others all give to something.
We all contributed something to the report.
Induct means "to allow someone to become a member of a group."
I was inducted into the Army.
There was an induction ceremony.
Home to. This is difficult. I would say, "He came home to me." This would indicate that this is his place, next to me. It is where he belongs.