A single global trademark does not exist. Trademark rights are territorial; protection applies only in the countries where the mark is registered.
The closest practical equivalent is using the Madrid System (WIPO), which allows a single international application to designate multiple member countries simultaneously. Over 130 countries participate in the system. Each designated country still examines the application under its own rules and can refuse it, but a single filing and a single renewal cover all designations.
For comprehensive coverage of your key markets, file nationally or through the Madrid System in the countries where you are commercially active or at greatest risk of brand copying.
Plan your international trademark strategy with Trama; free initial consultation available.