On a related list, How can i Ensure that only the person who initially created the record can edit it.
remove the permission view all modify all permission from profile set the OWD to private create a sharing rule and set it to read only and choose to whom you want to share the record
Remove Modify All Data from the Setup->Sharing setup on the object you wish to remove the edit permission apart from the record owner. Or the other way is to restrict the other users apart from record owner from editing the records by using Setup-> Account sharing rules and define the rules. Let me know how it worked