That sounds like an awesome game with the Mongols conquering Rome. Will you move to Lombardy or Austrasia to attempt to counter the Mongols further?
I started a game recently due to it being December and the Songs of Yuletide being enabled. Previously I'd played an HRE game and a Gascony-turned-Castile game; this time I decided to go for Italy from the earliest start. Started as Ravenna with Teuderic the Spider, and went from one county to a five-province duchy while scheming and defeating the Gates of Hell themselves. Tragedy would strike, however, with Teuderic's daughter-in-law dying in childbirth, and resulting in this unusual situation:
A duke who is literally a newborn, as the first child of the late duchess regnant. Conveniently, he was also my initial count's grandson. Thus, a couple generations down the line, I was ruling two duchies, one inherited, and one of which my ruler had ruled for literally his entire life. The Length of Rule bonus, even at a fairly young age, was significant, and it was a good thing too as some relatives were less than fully content with what they already had.
Europe looks interesting, with this screenshot being more or less still accurate:
France was mired in the Thirty Years' Civil War from 800 to 830, with Austrasia (Merovingian Middle Francia) eventually controlling most of the land. Saxony has had long-lived rulers and has been a notable power since early on, when Charlemagne suffered a severe wound in battle against them and died a few years later. Serbia has been powerful, but nearly every ruler has changed their religion (currently they are Orthodox, but Slavic and Tengrii has also been common). Islam has done well overall, especially in Iberia, though Lombardy controlled Tripolitania for a decade or two of near-constant warfare.
More recently, Duke Ago married his youngest son and heir (Ultimogeniture) to the future-and-now-current Duchess Regnant of Lombardy, who would then also inherit the Duchy of Benevento when her elder sister suffered an early death (which I didn't even play a hand in!). The King decided she then had too much power, and sought to revoke one of her counties. With my future grandson set to inherit the Duchy of Lombardy (unless the Duchess also died early, in which case her Sunni sister who had ruled Tripolitania would receive it; an interesting potentiality if one I didn't want), I threw my hat in with the rebelllion.
And it actually went swimmingly. I had not realized that, as of the current patch at least, a ruler who sought to revoke a province and lost the war was forced to resign, and Lombardy had a new King (though neither me nor the Duchess of Lombardy). Conveniently, it also lowered crown authority, freeing the way to continue my territorial expansion. And while I'd feared triggering the revoke-hammer at some point as had happened in my HRE game, I can now rest assured that so long as I'm allied with the Duchess of Lombardy, our provinces alone - which include all of Lombardy south of the screenshot as well - are more than enough to defeat the rest of the Kingdom.
Now it's 834, and after a couple wars with pesky vassal counts, my realm is well secured, so it's time to add another county here, another county there, while developing my lands. Eventually I'll move for a Kingdom, but there's no reason to rush it when the slow, methodical expansion is already working so well.