What separates the Karakoram Range, the Hindu Kush, and the Himalayan Range?
The River Indus in Jammu and Kashmir of India and Gilgit-Baltistan under Pakistan control is usually taken as the dividing line between Himalayas and Karakoram. 

The River Gilgit, a tributary of the Indus flowing from the North-west has its confluence with the Indus from the North-East near the town of Juglot or Jaglot about 45 km south east of Gilgit on the Karakoram Highway in Gilgit District and then the Indus flows south from here. 

The confluence between these rivers is known as "Tri Junction Point" or "Junction Point of Three Mountain Ranges". It is located at the junction of the 3 lofty mountain ranges, the Karakoram, Himalayas and Hindukush. 


To the North of this confluence or to the north of both Indus and Gilgit rivers is Karakoram. 
To the south  of the Indus before merger and to the East after merger are the Himalayas
To the south of Gilgit river and West of the merged Indus is Hindukush. 


In the Ladakh district of India, there is an east west range called the Ladakh range to the north of Indus, and sometimes this is taken as an extension of Karakorams. Beyond or to the north of Ladakh Range is the Shyok River, a tributary of Indus that flows westwards and joins the Indus near Skardu, and more commonly the mountains to the north of Shyok are called Karakoram range.