Among the array of heat exchangers available, printed circuit steam generators emerge as a particularly promising choice for high-temperature applications. This is primarily attributed to their augmented heat transfer surface area, which enables the efficient transfer of thermal energy within the Rankine power conversion cycle, especially in the context of molten salt-based thermal power systems, such as those employed in molten salt reactors and concentrated solar power plants. It is imperative to analytically model the heat transfer characteristics of mini-channel flow boilings for a printed circuit steam generator. To resolve new technical design issues that the single hot fluid flow channel is cooled by multiple cold fluid flow channels, an improved heat exchanger model is proposed to assist the numerical modeling of printed circuit steam generators for molten salt based on the equilibrium thermodynamics quality of water/steam flow. The existing flow boiling heat transfer coefficient correlations of mini-channels are leveraged to optimally design the straight-passage based printed circuit layouts and narrow down their optimal operational parameters. With various selections of subcooled water, saturated water, and superheated steam heat transfer correlations, The best combination of heat transfer correlations is found to assess the axial distributions of cold fluid temperatures and pressure drops. Two multi-objective optimizations are formulated to respectively solve thermal sizing and scaling problems for the optimal designs and operations of printed circuit steam generators. The computational results indicate that the overall heat transfer coefficient for an optimized 50 MW(th) printed circuit steam generator assessed at the transition point is about 3,828 W/(m2 K), which remarkably surpasses the 1,544 W/(m2 K) value of the conventional shell-tube steam generators by a factor of three. This implies that printed circuit steam generators would be a promising replacement of the traditional shell-tube steam generator.