Well I think ummm has answered this.
Next of kin is a term used on medical records. Also some bodies (eg care homes, employers) may record the name of a next of kin which I assume would be who they would contact in an emergency.
If you are an executor you will have some legal responsibilities. Apart from that I am not aware that you have any legal responsibilities.
If you have Power of Attorney then that gives responsibilities, but just because you are next of kin doesn't automatically give you that power.
So I'm still not sure what you mean by 'next of kin' in this case