PURPOSE: To develop and validate a data acquisition scheme combined with a motion-resolved reconstruction and dictionary-matching-based parameter estimation to enable free-breathing isotropic resolution self-navigated whole-liver simultaneous water-specific T 1 $$ {\mathrm{T}}_1 $$ ( wT 1 $$ {\mathrm{wT}}_1 $$ ) and T 2 $$ {\mathrm{T}}_2 $$ ( wT 2 $$ {\mathrm{wT}}_2 $$ ) mapping for the characterization of diffuse and oncological liver diseases. METHODS: The proposed data acquisition consists of a magnetization preparation pulse and a two-echo gradient echo readout with a radial stack-of-stars trajectory, repeated with different preparations to achieve different T 1 $$ {\mathrm{T}}_1 $$ and T 2 $$ {\mathrm{T}}_2 $$ contrasts in a fixed acquisition time of 6 min. Regularized reconstruction was performed using self-navigation to account for motion during the free-breathing acquisition, followed by water-fat separation. Bloch simulations of the sequence were applied to optimize the sequence timing for B 1 $$ {B}_1 $$ insensitivity at 3 T, to correct for relaxation-induced blurring, and to map T 1 $$ {\mathrm{T}}_1 $$ and T 2 $$ {\mathrm{T}}_2 $$ using a dictionary. The proposed method was validated on a water-fat phantom with varying relaxation properties and in 10 volunteers against imaging and spectroscopy reference values. The performance and robustness of the proposed method were evaluated in five patients with abdominal pathologies. RESULTS: Simulations demonstrate good B 1 $$ {B}_1 $$ insensitivity of the proposed method in measuring T 1 $$ {\mathrm{T}}_1 $$ and T 2 $$ {\mathrm{T}}_2 $$ values. The proposed method produces co-registered wT 1 $$ {\mathrm{wT}}_1 $$ and wT 2 $$ {\mathrm{wT}}_2 $$ maps with a good agreement with reference methods (phantom: wT 1 = 1 . 02 wT 1,ref - 8 . 93 ms , R 2 = 0 . 991 $$ {\mathrm{wT}}_1=1.02\kern0.1em {\mathrm{wT}}_{1,\mathrm{ref}}-8.93\kern0.1em \mathrm{ms},{R}^2=0.991 $$ ; wT 2 = 1 . 03 wT 2,ref + 0 . 73 ms , R 2 = 0 . 995 $$ {\mathrm{wT}}_2=1.03\kern0.1em {\mathrm{wT}}_{2,\mathrm{ref}}+0.73\kern0.1em \mathrm{ms},{R}^2=0.995 $$ ). The proposed wT 1 $$ {\mathrm{wT}}_1 $$ and wT 2 $$ {\mathrm{wT}}_2 $$ mapping exhibits good repeatability and can be robustly performed in patients with pathologies. CONCLUSIONS: The proposed method allows whole-liver wT 1 $$ {\mathrm{wT}}_1 $$ and wT 2 $$ {\mathrm{wT}}_2 $$ quantification with high accuracy at isotropic resolution in a fixed acquisition time during free-breathing.