In this position paper we discuss the potential evolution of Official Statistics from an operation model based on data concentration towards an alternative model based on computation spreading. The latter involves a certain degree of participation by the input data sources to the definition of the desired output information (statistics) as well as to the execution and design of the processing method. This approach reinforces the protection of confidentiality of the input data and distributes the physical and logical control over the whole process across multiple actors. This model can be naturally combined with the principles of public transparency, algorithmic transparency and audibility. Furthermore, the “shared control” spirit underlying this model fits well in scenarios where independent authorities are called to validate and certify the adherence of the computation instance to the applicable legal provisions (e.g., privacy regulations) and ethical standards. The collective effect of such measures is to increase transparency, collective control, public trust and acceptance over the use of increasingly pervasive deep data for public interest purposes.