Controlled by Parent access on child records
Key Takeaway
With "Controlled by Parent", a user's access to a child record matches their access to its parent record. Whatever they can do to the parent, they can do to the child, no matter who owns the child.
Controlled by Parent is an organization-wide default (OWD) setting. A child record with this setting has no sharing of its own. Instead, a user's access to the child record follows their access to the parent record it's linked to. If you can do something to the parent, you can do the same thing to the child. If you can't do it to the parent, you can't do it to the child. So you control what users can do with child records by controlling their access to the parent records.
How access to a child record works
Controlled by Parent is one of the OWD access levels in "Sharing Settings", alongside "Private", "Public Read Only" and "Public Read/Write". A record with this setting isn't shared on its own. A user can view, edit or delete it only if they can do that same action on its associated parent record.
Because the child record has no sharing of its own, the child's owner doesn't change the result. To give a user Read/Write access to child records that other users own, give the user Read/Write access to the parent record. The user then gets the same access to the child records.
In Dana's org, the Contact OWD is Controlled by Parent, so each contact's access follows its account. Dana can edit the Northwind account. Northwind has five contacts. Other reps own all five. Dana can edit all five contacts because she can edit Northwind. Later, Dana's access to Northwind changes to read only. Now she can view the five contacts, but she can't edit them.