We would like to be able to tag a task to a secondary object and/or record.   Is there a setting depending on where the task is created?  

For example:

If crated under a contact, automatically save to the account as well?

If created under a a case, automatically save to the account as well?

I know that if you create an opportunity, it automatically saves to the account.  How can we get this similar logic to flow to contact and case?