What is the ruling on one who says to his wife: "By Allah the Almighty, I will never come near you at all, completely. You are no longer of any concern to me"?

If the phrase "I will not come near you" means abstaining from conjugal relations with the wife, then this constitutes an ila' (vow of abstinence), and its consequences apply if the husband intended to abstain from intercourse. If four months pass without intercourse, the wife has the right to refer her case to the judge, who will order the husband to either divorce or engage in intercourse. In the case of intercourse, he is liable for an expiation for breaking an oath (kaffarat yamin). As for the phrase "That's it, you are no longer binding upon me," it is an allusive divorce (kinayat talaq); if he intended divorce by it, then it is effective. The ruling for both phrases depends on the husband's intention.