Researchers pay special attention to the problem of parents' attitude to the activity of children and adolescents in the Internet and their influence on this activity. The reason for such detailed study of this issue is the increasing processes of digitalization, including due to the COVID-19 pandemic. We have conducted a survey among high school pupils in Perm region. In this article, based on the data obtained, we create a classification of parenting styles in their stance to pastime of their children in the Internet and identify the factors that determine a particular style of behavior.The study showed that there are two groups of such factors. One group is the characteristics of children (gender, class, academic performance); the other group is the characteristics of the family (the number of children in the family, family living standards, the availability of digital devices, the use of information and communications technology by parents). The predominant parenting style is the absence of restrictions. At the same time, the use of a restrictive style doesn't lead to a significant decrease in pastime of high school pupils in the Internet.