Fine mesh of Local block methods.
 

If it is needed to create the fine (hexahedral) mesh in a region by blocking strategy I found the 4 methods:
I Strategy:
1) Create the blocks on the geometry;
2) Check their right connectivity (merge vertices) and use check blocks;
3) Cross-sectionaly convert some blocks to swept type;
4) Set free face mesh type to All Quad;
5) Fine the edge bunching parameters and find their ratios to avoid the triangular mesh;
6) Pre-mesh-> convert to unstructured.
+ Allow to create entirely hexahedral mesh with highest refinement in a region;
- Special need to check the topology of swept blocks and need to find the edge bunching parameters in spite of All Quad setting on the free faces (???).
II Strategy:
1) Create the blocks on the geometry;
2) Check their right connectivity (merge vertices) and use check blocks;
3) Create O-grid in this refinement region;
4) In case of problem of o-grid creation, activate only VORFN-part and delete visible blocks after repeat creation of O-grid;
5) Pre-mesh-> convert to unstructured.
+ Allow to create up to 3 times more elements in a region;
- robust O-grid method and possible low quality elements in o-grid region;
III Strategy:
1) Create the blocks on the geometry;
2) Check their right connectivity (merge vertices) and use check blocks;
3) Convert some blocks to free type and set their type;
4) Convert free blocks faces to free type and set their type;
5) Set free blocks faces’ edges bunching parameters;
6) Pre-mesh-> convert to unstructured.
+ Allow to create highest refinement in a region;
- doesn’t allow to create entirely hexahedral elements, no topology in this region.
IV Strategy:
1) Create the blocks on the geometry;
2) Pre-mesh params-> refinement;
3) Pre-mesh-> convert to unstructured.
+ Allow to create highest refinement in a region and entirely hexahedral mesh;
- doesn’t allow to undo the refinement and it is created the hanging-nodes on the element edges.
The first strategy, seems the best way. Possible somebody have another point of view at least on how to change the bunching level on some edges on the same level of blocks.