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Purpose: Volumetric, high-resolution, quantitative mapping of brain tissue relaxation properties is hindered by long acquisition times and signal-to-noise (SNR) challenges. This study, for the first time, combines the time-efficient wave-CAIPI readouts into the 3D-quantification using an interleaved Look-Locker acquisition sequence with a T2 preparation pulse (3D-QALAS) acquisition scheme, enabling full brain quantitative T1, T2 and proton density (PD) maps at 1.15 mm3 isotropic voxels in only 3 minutes. Methods: Wave-CAIPI readouts were embedded in the standard 3D-QALAS encoding scheme, enabling full brain quantitative parameter maps (T1, T2, and PD) at acceleration factors of R=3x2 with minimum SNR loss due to g-factor penalties. The quantitative parameter maps were estimated using a dictionary-based mapping algorithm incorporating inversion efficiency and B1 field inhomogeneity. The quantitative maps using the accelerated protocol were quantitatively compared against those obtained from conventional 3D-QALAS sequence using GRAPPA acceleration of R=2 in the ISMRM NIST phantom, and ten healthy volunteers. Results: When tested in both the ISMRM/NIST phantom and ten healthy volunteers, the quantitative maps using the accelerated protocol showed excellent agreement against those obtained from conventional 3D-QALAS at RGRAPPA=2. Conclusion: 3D-QALAS enhanced with wave-CAIPI readouts enables time-efficient, full brain quantitative T1, T2, and PD mapping at 1.15 mm3 in 3 minutes at R=3x2 acceleration. When tested on the NIST phantom and ten healthy volunteers, the quantitative maps obtained from the accelerated wave-CAIPI 3D-QALAS protocol showed very similar values to those obtained from the standard 3D-QALAS (R=2) protocol, alluding to the robustness and reliability of the proposed methods.