Georges Roux, in his book Ancient Iraq (Third edition, p. 68), says that
The city of Uruk was born of the coalescence of two towns 800 metres apart: Kullaba, devoted to the sky-god An (or Anu), the supreme god of the Mesopotamians, and E-Anna ('House of Heaven'), the main abode of the love goddess Inanna (called Ishtar by the Semites).
Is this the first historical example of conurbation? (For those of you who don't know, conurbation is the process of physical coalescence of cities)
I think you are right. It probably is the first historical example of conurbation, subject to an important caveat:
The merge has to involve large towns or cities before it's considered to be conurbation.
There were almost certainly earlier merges of smaller settlements - villages or hamlets combining to form small towns etc., but for the purpose of the definition, these don't count as conurbation.
Uruk is certainly one of the earliest cities. As you say, Georges Roux observed that it was formed by the coalescence of the towns of Kullaba and Eanna. I don't think any of the other early cities developed from the conurbation of two earlier large settlements. So yes, based on that, Uruk is the first historical example of conurbation.
