This work presents a comprehensive VERDICT prostate model (relaxed-VERDICT) that includes compartment-specific relaxation effects providing prostate microstructural estimates unbiased by the relaxation properties of the tissue. We compare relaxed-VERDICT with the original VERDICT model and use it to provide estimates of T2 and T1 in benign and tumor prostate tissue. Our results suggest that original VERDICT’s fic contrast is mostly driven by diffusion, supporting its use as imaging marker of apparent cellular volume fraction. Relaxed-VERDICT estimates of T1/T2 values are in very good agreement with literature. Finally, we propose a machine learning based processing pipeline that provides ultra-fast quantitative maps.