State is society’s need for the existence of an organized power, equipped with the right equipments of coercion and able to run the society, by imposing the choices that seem reasonable to them, through legal norms. State is an organization of state power; it is an organized power which imposes its will to all the society and has a whole mechanism to execute this will. The state realizes its functions through power, which is a mechanism to accomplish its relevant functions. The power’s concept is a social concept, which can be understood only as a relation between two subjects, between two wills. Power is the ability to impose an order, a rule and other’s behavior in case that he doesn’t apply voluntary the relevant norm, respectively the right. Using state power is related to creation and application, respectively the implementation of law. To understand state power better, we have to start from its overall character. So, we notice that in practice we encounter different kinds of powers: the family’s one, the school’s one, the health’s one, the religion’s, culture’s etc. The notion of powers can be understood as a report between two subjects, two wills. Power is an order for other’s behavior. Every power is some kind of liability, dependence from others. In the legal aspect, supremacy of state presents the constitutive – legislative form upon the powers that follow after it. Supremacy, respectively the prevalence, is stronger upon other powers in its territory. For example we take the highest state body, the parliament as a legislative body, where all other powers that come after it, like the executive and court’s one, are dependable on state’s central power. We can’t avoid the carriage of state’s sovereignty in the competences of different international organizations. Republic, based on ratified agreements for certain cases can overstep state’s power on international organizations. The people legitimate power and its bodies, by giving their votes for a mandate of governance (people’s verdict). It is true that we understand people’s sovereignty only as a quality of people, where with the word people we understand the entirety of citizens that live in a state. The sovereignty’s case actualizes especially to prove people’s right for self-determination until the disconnection that can be seen as national – state sovereignty. National sovereignty is the right of a nation for self-determination. Sovereignty’s cease happens when the monopoly of physical strength ceases as well, and this monopoly is won by another organization. A state can be ceased with the voluntary union of two or more states in a mutual state, or a state can be ceased from a federative state, where federal units win their independence. In this context we have to do with former USSR’s units, separated in some independent states, like Czechoslovakia unit that was separated in two independent states: in Czech Republic and Slovakia. Former Yugoslavia was separated from eight federal units, today from these federal units seven of them have won their independence and their international recognition, and the Republic of Kosovo is one amongst them.
 Every state power’s activity has legal effect inside the borders of a certain territory and inside this territory the people come under the relevant state’s power. Territorial expansion of state power is three dimensional. The first dimension includes the land inside a state’s borders, the second dimension includes the airspace upon the land and the third dimension includes water space. The airspace upon inside territorial waters is also a power upon people and the power is not universal, meaning that it doesn’t include all mankind. State territory is the space that’s under state’s sovereignty. It is an essential element for its existence. According to the author Juaraj Andrassy, state territory lies in land and water space inside the borders, land and water under this space and the air upon it. Coastal waters and air are considered as parts that belong to land area, because in every case they share her destiny.
 Exceptionally, according to the international right or international treaties, it is possible that in one certain state’s territory another state’s power can be used. In this case we have to do with the extraterritoriality of state power. The state extraterritoriality’s institute is connected to the concept of another state’s territory, where we have to do with diplomatic representatives of a foreign country, where in the buildings of these diplomatic representatives, the power of the current state is not used. These buildings, according to the international right, the diplomatic right, have territorial immunity and the relevant host state bodies don’t have any power. Regarding to inviolability, respectively within this case, we have two groups to mention: the real immunity and the personal immunity, which are connected with the extraterritoriality’s institute.
 Key words: Independence, Sovereignty, Preponderance, Prevalence, Territorial Expansion.
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