Purpose: To achieve free-breathing quantitative fat and R * 2 mapping of the liver using a generalized model-based iterative reconstruction, dubbed as MERLOT. Methods: For acquisition, we use a multi-echo radial FLASH sequence that acquires multiple echoes with different complementary radial spoke encodings. We investigate real-time single-slice and volumetric multi-echo radial FLASH acquisition. For the latter, the sampling scheme is extended to a volumetric stack-of-stars acquisition. Model-based reconstruction based on generalized nonlinear inversion is used to jointly estimate water, fat, R * 2 , B0 field inhomogeneity, and coil sensitivity maps from the multicoil multi-echo radial spokes. Spatial smoothness regularization is applied onto the B0 field and coil sensitivity maps, whereas joint sparsity regularization is employed for the other parameter maps. The method integrates calibration-less parallel imaging and compressed sensing and was implemented in BART. For the volumetric acquisition, the respiratory motion is resolved with self-gating using SSA-FARY. The quantitative accuracy