We devise a strategy in order to generate large-size adapted tetrahedral anisotropic meshes, having O(10^8-10^9) elements, as required in many fields of application in scientific computing. We target moderate scale parallel computational resources as typically found in R\&D units where the number of cores ranges in 10^2-10^3. Both distributed and shared memory architectures are handled. Our strategy is based on typical domain splitting algorithm where the initial mesh is split in parts that are then meshed in parallel while the fictitious boundaries between parts are kept unchanged. Then we iterate the procedure to adapt previously unmodified parts of the domain, {\it i.e.}, the interface mesh. Both the volume and the surface meshes are adapted simultaneously and the efficiency of the method is independent of the complexity of the geometry. The originality of the method relies on (i) a metric-based static load-balancing, (ii) hierarchical mesh partitioning techniques to (re)split the (complex) interfaces meshes, (iii) a fast, robust and generic sequential cavity-based mesh modification kernel. In order to generate large-size meshes, out-of-core storing of completed parts is used to reduce the memory footprint. %Among the difficulties of this method include (i) an efficient remeshing of the interfaces between partitions, (ii) preserving the load-balancing and (iii) ensuring the robustness of the whole process. We show that we are able to generate (uniform, isotropic and anisotropic) meshes with more than 1 billion tetrahedra in less than 20 minutes on 120 cores. Examples from Computational Fluid Dynamics (CFD) simulations are also discussed.