Abdominal T1 mapping has been used for the quantification of various pathologies including the characterization of focal liver lesions and liver fibrosis. The presence of fat and iron in the liver act as confounding factors resulting in T1 estimation errors. In this work, we present a multi-echo inversion-recovery radial Look-Locker technique with FLASH readouts for simultaneous T1w, T2* and PDFF quantification. We also propose two fitting strategies to generate water-only T1 estimates from the acquired data. Performance of the method is evaluated on phantoms and in vivo results are presented.