Does the .xn--mgba3a4f16a domain exist?

Yes. .xn--mgba3a4f16a is a live top-level domain in the IANA root zone.

Does .ایران (.xn--mgba3a4f16a) exist?

Yes. .ایران (.xn--mgba3a4f16a) is a real top-level domain, live in the IANA root zone right now.

See the .ایران (.xn--mgba3a4f16a) page for what kind of TLD it is. Note that existing in the root doesn’t always mean anyone can register one — some TLDs are brand-restricted.

Try to register a .ایران (.xn--mgba3a4f16a) domain

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This answer is generated from the live IANA root zone list, not from vibes. If the DNS changes, this page changes.