In other words, Genoa's expansion in CK2 would just be perfect if only it didn't acquire any territory along the way. Take a look at this map which I craftily hotlinked from Wikipedia:
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They sent their merchants on the merry way to basically everywhere, but even at its peak, their actual territory was limited to Liguria, Corsica and northern Sardinia, along with some outposts on the Aegean islands and the Crimean coastline, which they gained in the Fourth Crusade. Their influence, however, was much, much greater than that. They easily dominated the economics in the Western Mediterranean, and later, all around the Black Sea.
It would be rather nice, I think, if Genoese and Venetian (or other Republics') merchants could build trading posts in empty barony slots (similarly to how the Knights Templar etc. gain their holdings), and somehow get involved in local politics (for example, claiming the entire county afterwards).
Thats funny because the trading post idea was originally planned as a feature for Ck2, and is 99% certain to be the in the upcoming Republics DLC