We investigated public acceptance of conditionally automated (SAE Level 3) passenger cars using a questionnaire study among 9,118 car-drivers in eight European countries, as part of the European L3Pilot project. 71.06% of respondents considered conditionally automated cars easy to use while 28.03% of respondents planned to buy a conditionally automated car once it is available. 41.85% of respondents would like to use the time in the conditionally automated car for secondary activities. Among these 41.85%, respondents plan to talk to fellow travellers (44.76%), surf the internet, watch videos or TV shows (44%), observe the landscape (41.70%), and work (17.06%). The UTAUT2 (Unified Theory of Acceptance and Use of Technology) was applied to investigate the effects of performance and effort expectancy, social influence, facilitating conditions, and hedonic motivation on the behavioural intention to use conditionally automated cars. Structural equation analysis revealed that the UTAUT2 can be applied to conditional automation, with hedonic motivation, social influence, and performance expectancy influencing the behavioural intention to buy and use a conditionally automated car. The present study also found positive effects of facilitating conditions on effort expectancy and hedonic motivation. Social influence was a positive predictor of hedonic motivation, facilitating conditions, and performance expectancy. Age, gender and experience with advanced driver assistance systems had significant, yet small (<0.10), effects on behavioural intention. The implications of these results on the policy and best practices to enable large-scale implementation of conditionally automated cars on public roads are discussed.