What happens to a minor if he threatened to hurt or kill someone in a heated argument on the phone?

Don't say anything to the police or anyone else about the case until you speak with a lawyer. Be proactive and retain a lawyer now; one that predominantly practices criminal defense.

Most likely, nothing will come of this, but I would need more information to know for sure. A threat of this nature may be incorporated into a larger offense of stalking, or possibly an assault if the threat put the other person in a reasonable fear for their safety. It is unlikely that a prosecutor would choose to prosecute such an occurrence unless the threats were very credible and serious.

Need specifics, but nothing good can be expected. See an attorney with the details.