Fetal MRI is widely used for quantitative brain volumetry studies. However, currently, there is a lack of universally accepted protocols for fetal brain parcellation and segmentation. Published clinical studies tend to use different segmentation approaches that also reportedly require significant amounts of time-consuming manual refinement. In this work, we propose to address this challenge by developing a new robust deep learning-based fetal brain segmentation pipeline for 3D T2w motion corrected brain images. At first, we defined a new refined brain tissue parcellation protocol with 19 regions-of-interest using the new fetal brain MRI atlas from the Developing Human Connectome Project. This protocol design was based on evidence from histological brain atlases, clear visibility of the structures in individual subject 3D T2w images and the clinical relevance to quantitative studies. It was then used as a basis for developing an automated deep learning brain tissue parcellation pipeline trained on 360 fetal MRI datasets with different acquisition parameters using semi-supervised approach with manually refined labels propagated from the atlas. The pipeline demonstrated robust performance for different acquisition protocols and GA ranges. Analysis of tissue volumetry for 390 normal participants (21-38 weeks gestational age range), scanned with three different acquisition protocols, did not reveal significant differences for major structures in the growth charts. Only minor errors were present in < 15% of cases thus significantly reducing the need for manual refinement. In addition, quantitative comparison between 65 fetuses with ventriculomegaly and 60 normal control cases were in agreement with the findings reported in our earlier work based on manual segmentations. These preliminary results support the feasibility of the proposed atlas-based deep learning approach for large-scale volumetric analysis. The created fetal brain volumetry centiles and a docker with the proposed pipeline are publicly available online at https://hub.docker.com/r/fetalsvrtk/segmentation (tag brain bounti tissue).