First of all, I would like to clarify that a Hindu Undivided Family cannot exist within a Hindu Undivided Family. It is a continutation and the members keep getting added to it. Karta is the head of the Hindu Undivided family. Birth of new members does not create a new Hindu Undivided Family but just adds them to the existing one. Therefore, the Karta remains the one who was Karta before their birth. Therefore, in your case, you need to understand that there is only one HUF and only one Karta, i.e, K when he was alive. There can not be another HUF arising from the original one, unless the first one was dissolved via Partition between the concerned members. Hence, unless a Partition took place on the application of N, N doesn't become a Karta of another HUF for there is no new HUF, simpy put.
When K died in 2002, N being his only son, naturally becomes the Karta of the single HUF.