Purpose: To develop a novel quantitative method for detection of different tissue compartments based on bSSFP signal profile asymmetries (SPARCQ) and to provide a validation and proof-of-concept for voxel-wise water-fat separation and fat fraction mapping. Methods: The SPARCQ framework uses phase-cycled bSSFP acquisitions to obtain bSSFP signal profiles. For each voxel, the profile is decomposed into a weighted sum of simulated profiles with specific off-resonance and relaxation time ratios. From the obtained set of weights, voxel-wise estimations of the fractions of the different components and their equilibrium magnetization are extracted. For the entire image volume, component-specific quantitative maps as well as banding-artifact-free images are generated. A SPARCQ proof-of-concept was provided for water-fat separation and fat fraction mapping. Noise robustness was assessed using simulations. A dedicated water-fat phantom was used to validate fat fractions estimated with SPARCQ against gold-standard 1H MRS. Quantitative maps were obtained in knees of six healthy volunteers, and SPARCQ repeatability was evaluated in scan rescan experiments. Results: Simulations showed that fat fraction estimations are accurate and robust for signal-to-noise ratios above 20. Phantom experiments showed good agreement between SPARCQ and gold-standard (GS) fat fractions (fF(SPARCQ) = 1.02*fF(GS) + 0.00235). In volunteers, quantitative maps and banding-artifact-free water-fat-separated images obtained with SPARCQ demonstrated the expected contrast between fatty and non-fatty tissues. The coefficient of repeatability of SPARCQ fat fraction was 0.0512. Conclusion: The SPARCQ framework was proposed as a novel quantitative mapping technique for detecting different tissue compartments, and its potential was demonstrated for quantitative water-fat separation.