Ok, since I got not that many replies, let me show you what I'm talking about...
It all starts with these small (around 1 mm in length) bulbils that gorw on the top of the mature bulbs.
In fact these are new plants.
Later they get roots and develop into this tiny plant.
I asked advise from a lady who is, probably, the most expert orchid grower in my country, and she told me to keep them in the mother plant, even during their rest.
When replanting (around Jan/Feb) separate them from the mother plant and pot them. They are expected to bloom after 3 years (in avg).