First of all understanding of what a common space is is crucial for looking at examples of those that are global. A classic example of a common area is common grazing land within a community but the questions you then need to ask are:
Can anyone access the commons? - in some cases YES, a total free-for-all but in other cases they belong to a community.
Can you do anything in the commons? For example you may be allowed to graze but not to build infrastructure.
Are there limits on inidividual use so that all can use it? This is relevant if the commons has exhautible resources.
Does the community of users 'own' the commons to the point that they can it oss (to one of their own or others)?
Is all enforcement on the commons official?
Is it nobody's or everybody's?
Therefore we can then think about the global commons which are common areas at a global scale. All parts of the planet with permanent settlement are bound within soverign state territories and therefore at the global scale land is not common. However there are spaces on the Earth that have one of more global common properties, these include: ocean (water and sea-bed), air (inner atmosphere and outer space) and celestial bodies and Antarctica.
The oceans as a global commons is complicated as they are a mix of inexhaustible and exhaustible (e.g. fish) resources and they also have coastal interests (e.g. ecosystem services the ocean provides). The resources in the ocean are separated at different depths, for example ships on the surface providing transport, fish in the water column and oil rigs tapping into resources below the sea bed. The 1982 UN Convention on the Law of the Sea and divides the ocean into four key regions. 1. Territorial Waters (0-12 nautical miles from land), this is not common but a common right to naviagation is recognised and is therefore an extension of the territory (the ships do not have a right to dock etc... but they have the right to innocent passage). 2. Exclusive economic zone (12-200 nautical miles), common but the coastal state has exclusive right to exhaustible resources. Policing here is different to area 1 as police are not allowed to board ships unless they have reasons such as: piracy, slave trade, illegal broadcasting or they believe the ship is sailing under a different flag. 3. High Seas (waters beyond 200 nautical miles) have common access and use but there is no sharing requirement. 4. International Sea Bed (seabed beyond 200 nautical miles) has common access and use but must benefit everyone with the implementation of a sharing mechanism (this includes financial benefits and technological know-how).
Air is a global commons although cannot be described as infinite due to pollution. The geostationary orbit is a narrow stips of space and things in this space will move at the same speed as Earth such as satellites. This is a space that everyone can use however, due to legal requirements about spacing between objects it is a finite resource. The Inner Atmospheric air space is the same as territorial waters, it is not common but there is a common right to navigation. Outer space on the other hand is a common spacebut the Outer Space Treaty outlined some rules. There is a ban on militarisation therefore does not allow weapons on celestial bodies but it does allow conventional weapons in orbit, satellites and drones fall under this category. Economic ativity if allowed but it must benefit all but does not need to be shared except in the Moon Treaty, for example in the future mining of asteroids or water extraction from planets.
Many state Antarctica as a global commons however, is one of the worst examples. Unlike other spaces already looked at this space is land so is conceivably terriroty. The area was not seen by man until approximately 1820, it has a harsh climate and as it has no indigenous population the only ones that inhabit the continent are between 1000 and 5000 scientiest depending on the season. Before the treaty seven states made claims to portions of Antarctica (New Zealand, Australia, Argentina, Chile, UK, Norway and France). As Antarctica became a site of impotrance for militarization during the Cold War it's ecological state was put under threat and therefore a treaty was created in 1959. This froze the existing seven claims, banned military or economic activity and allowed any state to conduct research anywhere. Therefore Antarctica is common in terms of access and science but not common as ownership of certain sections is recognized.