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This article aims to examine how the theory of co-production can be connected with servitization and digitalisation and used together for the public service development with the help of discrete-event simulation modelling to highlight time-related deficiencies of a complex public service process, which is most commonly used by patchwork families. Data was taken from the Guardianship Office in Győr (Hungary), based on which in-depth interviews were conducted. Based on the legal background and the interviews, the authors of the article created the process model of the contacting procedure. Based on the model, discrete-event simulation was used to identify the process elements for potential improvement through servitization. Discrete-event simulation showed the insufficiency of national regulation regarding the whole process and weaknesses of the contacting procedures in terms of quality and success. Basic reasons were found for the dissatisfaction expressed by participants of the procedures (administrators and customers). The increasing customer demand for high quality and efficient public services and failures in the New Public Management (NPM) in Eastern European countries require other approaches to advance. The paper connects the theory of co-production and servitization in a public service context and demonstrates how a complex public service can be examined with this approach to find possible improvements. The government must change the process regulation considering the number of the cases, the workload of administrators and family types (divorced or patchwork). The emphasis should be placed on the training and experience of administrators.