The Greater Coucal- Centropus sinensis has been split in ( Rasmussen & Anderton 20005) and alongwith 16 other species are not elevated to Species status, because they are Provisionally split. They are only referred as Sub-species.
Centropus sinenis sinensis, is the Nominate race.( Greater Coucal)
Centropus sinensis parroti is the sub-species split.( Southern Coucal)
There is no third species.
These can be ascertained from the recent publication of Oxford " Birds of Indian Subcontinent" auhthored by Richard Grimmet & Carol Inskipp, Second Edition brought out last month.
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