It starts on my page 113, an isolated Esmenet section in TJE, Ch. 3. I was reminded of this thread as I am rereading TAE (I'm nearly done TJE now) and thought I'd respond as I'm actually slinking through the threads once.
In broad strokes, Kellhus seems to continue straight on south from Shimeh onto Nilnamesh and to Angvaishi (sp?), the fortress on Zeum's mountainous border. It'd seem obvious that as Dunyain - the "ultimate" tactician - and with the star-studded attendence at Shimeh's coronation, that Kellhus would also secure Momemn and Nansur with the recency of Conphas' death. Esmenet reflects in the aforementioned passage, as I recall, that Momemn alone capitulated to Kellhus and the Zaudunyani without resistance. The text says that Theliopa (the second after Kayutas at Shimeh) was born fighting the Nilnamesh but Serwa was born fighting in Carythusal, Momemn yielding somewhere in between.
Also as Sorweel's reflects during WLW, I believe, with his fellow Scions, that their fathers are those whose nations and city-states surround the Three-Seas but haven't totally capitulated. And there are the few wildcards, my personal favorite nugget being "the legendary campaign of bribery and assassination whereby King Eselos Mursidides stole Cironj from the Orthodox." Lol, damn, right?
Also, we can date the Unification Wars to only lasting nine years after the end of the Holy War because in TJE it's stated that the Sranc Bounty and the preparation of the Great Ordeal occurred eleven years before TJE's current events, cleanly dividing the intervening twenty (assuming Kellhus only starting preparing in earnest after the conclusion of the Unification Wars).