Novel methods for quantitative, transient-state multiparametric imaging are increasingly being demonstrated for assessment of disease and treatment efficacy. Here, we build on these by assessing the most common Non-Cartesian readout trajectories (2D/3D radials and spirals), demonstrating efficient anti-aliasing with a k-space view-sharing technique, and proposing novel methods for parameter inference with neural networks that incorporate the estimation of proton density. Our results show good agreement with gold standard and phantom references for all readout trajectories at 1.5 T and 3 T. Parameters inferred with the neural network were within 6.58% difference from the parameters inferred with a high-resolution dictionary. Concordance correlation coefficients were above 0.92 and the normalized root mean squared error ranged between 4.2 and 12.7% with respect to gold-standard phantom references for T1 and T2. In vivo acquisitions demonstrate sub-millimetric isotropic resolution in under five minutes with reconstruction and inference times < 7 min. Our 3D quantitative transient-state imaging approach could enable high-resolution multiparametric tissue quantification within clinically acceptable acquisition and reconstruction times.