The future of our country depends on the efficiently developed higher education system that meets the needs of the country's development, the demands of modern life, and the interests of the individual. In their activities, higher education institutions pay considerable attention to the problems of forming a contingent of higher education applicants, since the presence of students is a key factor in the functioning of the university as a business entity. Therefore, today the competition of higher education institutions for the flow of applicants is quite relevant. The authors studied the system of attracting a contingent of students in foreign universities and identified the features of its formation in domestic higher education institutions. The main components of the process of forming a contingent of students in domestic higher education institutions are identified and a comparative analysis is made of the system of selection among applicants, which differs significantly from the European one. In Ukraine, the state order in higher education institutions is differentiated by competitive offers: "fixed", which provides for a certain number of state-funded places and can be used by applicants with the highest scores; "open", available to all applicants across all higher education institutions. The "open" competition proposal is considered "targeted placement of the state order": state-funded places go to the best applicants, and are not distributed among higher education institutions. According to the study results, the majority of researchers and teaching staff support the formation of a contingent of higher education students on the following principle: the Ministry of Education and Science of Ukraine creates budget places, while higher education institutions create contract places. Today, the Ministry of Education and Science of Ukraine uses the principle of formulaic distribution of the state order. This means that state places are allocated to the best applicants, and the number of higher education students is determined by the licensed volume for a certain level of higher education or a certain educational program.