Data transformations in hierarchical classification
It depends on the dataset, but generally fit again

why? If you dont fit again on the second level when classifying 1.1 and 1.2 you are introducing bias that you got from the first level when you classified between classes 1 and 2.

why it depends? if information is intertwined between all of the parent and children classes and you will use these models again in the future, you could be loosing important information when fitting again, in other words you will be only over-fitting on the current train (classify 1.1 1.2)