In blender 2.79 in the Outliner you can right click a parent object and delete all child objects by right clicking and select delete hierarchy.
In 2.80 I don't seem to be able to do this as I only see delete. The "delete hierarchy" option is not there.
I have changed Outliner to 'Scene' type view mode.. not the 'Collections' mode it defaults to.
FYI - "Delete Hierarchy" still exists, but only for collections - as mentioned is missing for objects.
Related to this (an example why this is still needed): 1. File > New > General (creates the original cube) 2. Switch to edit mode (modify or not the original cube) 3. Add > cube (accidentally in edit mode)
The added cube is a child of the original cube. This child cube automatically gets a material child - without doing any shading or such.
Once created this way, there seems to be no way to delete it from the hierarchy. Selecting the child cube object, also selects the parent. Using delete here will delete the parent too. Likewise deleting the child from the outliner hierarchy will also delete the parent.
Selecting the child vertices in edit mode, then deleting vertices or faces will delete the visible object. But there will be the empty object still in the hierarchy of the outliner. You can delete the material, but it seems to be still lurking around unused.
Also just after creating the child cube, you select it in the outliner, it becomes attached to the original cube (both same size). Then there is no way to select the child to move or modify it independently.
Also you will note, that both cubes are named "Cube". In other instances, I have seen this happen when intentionally creating child objects in the edit mode. This seems to confuse things - editing one of the same name will edit both.
The old method of shift-g > children and then alt-p to un-parent also seems not to work - or do anything obvious.
The only solution is to delete the parent and start over. This time being careful to be in object mode instead of edit mode. Save often (every edit?) so you can revert!
In general the UI menus lack interlocks (gray out/disable) where actions are inappropriate or will have no effect. You will also note that most menu items of the outliner say "(undocumented operator)" - probably means the help text is missing. My guess would be that this menu is not yet fully developed.
