To achieve dynamic water/fat separation and field inhomogeneity mapping via model-based reconstructions of undersampled triple-echo multi-spoke radial FLASH acquisitions. This work introduces an undersampled triple-echo multi-spoke radial FLASH sequence, which uses (i) complementary radial spokes per echo train for faster spatial encoding, (ii) asymmetric echoes for flexible and nonuniform echo spacing, and (iii) a golden angle increment across frames for optimal k-space coverage. Joint estimation of water, fat, inhomogeneity, and coil sensitivity maps from undersampled triple-echo data poses a nonlinear and non-convex inverse problem which is solved by a model-based reconstruction with suitable regularization. The developed methods are validated using phantom experiments with different degrees of undersampling. Real-time MRI studies of the knee, liver, and heart are conducted without prospective gating or retrospective data sorting at temporal resolutions of 70, 158, and 40ms, respectively. Up to 18-fold undersampling is achieved in this work. Even in the presence of rapid physiological motion, large field inhomogeneities, and phase wrapping, the model-based reconstruction yields reliably separated water/fat maps in conjunction with spatially smooth inhomogeneity maps. The combination of a triple-echo acquisition and joint reconstruction technique provides a practical solution to time-resolved and motion robust water/fat separation at high spatial and temporal resolution.