Considering the large prevalence and frequent use of smartphones among children and the very small number of studies on the impact of smartphone use on conflicts and the quality of child-parent relationships, the purpose of this research is to examine the connection between the quality of child-parent relationships and conflicts over the use of smartphones between children and parents. 281 students participated in the research, of which 168 were girls and 113 were boys. To measure the time a child spends using a smartphone, to measure conflict in the child-parent relationship, and to measure sociodemographic characteristics, measures constructed for the needs of the HRZZ project "Digital technology in the family: patterns of behaviour and effects on child development" were used in this work. The Smartphone Addiction Scale (Kwon et al., 2013) was used to measure smartphone addiction risk. The Child-Parent Relationship Scale (Hair et al., 2005) was used to measure the quality of the child-parent relationship. This research confirmed the positive association between children's smartphone use time and the risk of smartphone addiction in children. A positive association of the risk of smartphone addiction with conflicts over smartphone use between children and parents was also confirmed, but the connection between the time of use and conflicts over use was not confirmed. The negative association of risk for addiction with identification with parents and parental support was confirmed, but the association of time of use with identification with parents and parental support was not confirmed. The negative association of identification with parents and parental support with conflicts about use between children and parents was confirmed. The existence of a direct and statistically significant contribution of identification with parents and parental support to the explanation of conflict in the child-parent relationship regarding smartphone use was confirmed. The results of the regression analyzes showed the existence of an indirect and significant contribution of identification with parents and parental support through the risk of smartphone addiction, but not through the time of smartphone use, to the explanation of conflict in the child-parent relationship regarding smartphone use.