The recent development of new and innovative home battery systems has been seen by many as a catalyst for a solar energy revolution, and has created high expectations in the sector. Many observers have predicted an uptake of combined PV/battery units which could ultimately disconnect from the grid and lead to autonomous homes or micro-grids. However, most of the comments in social media, blogs or press articles lack proper cost evaluation and realistic simulations. We aim to bridge this gap by simulating self-consumption in various EU countries, for various household profiles, with or without battery. Results indicate that (1) self-consumption is a non-linear, almost asymptotic function of PV and battery sizes. Achieving 100% self-consumption (i.e. allowing for full off-grid operation) is not realistic for the studied countries without excessively oversizing the PV system and/or the battery; (2) although falling fast, the cost of domestic Li-Ion storage is most likely still too high for a large-scale market uptake in Europe; (3) home battery profitability and future uptake depend mainly on the indirect subsidies for self-consumption provided by the structure of retail prices; (4) the self-sufficiency rate varies widely between households. For a given household, the volume of self-consumption cannot be predicted in a deterministic way. Along with these results, this study also provides a database of synthetic household profiles, a simulation tool for the prediction of self-consumption and a method for the optimal sizing of such systems.