Well, as long as it's not that old since you bumped it...
You mean their glorified raids? I mean yeah they went as far as Nicea and they captured a good deal of cities but they lost them exceedingly quickly afterwords. I don't really have much faith in them compared to Candar or Aydin.
Or via a coalition of other Beyliks. The Ottomans were making quite a scene when they took Karesi out, the other beyliks would most certainly ally against them afterwords and probably win without the extra resources of the Balkans or Murad's leadership.
If Timum wipes out not only Bayezid but his sons and thus the succession, it could lead toa civil war during which Bulgaria might well manage to win its war of independence - which lasted till the 1420s even OTL. If enough turmoil can occur that the Karaminids can come in, such a Bulgaria might be able to consolidate and be the power that helps unite the Balkans.
One impact this would have is that another group might be more amenable to letting Western traders through to the East. Now, if there's a lot of civil strife in the near term, you could even see a different route looked for early. (Constantinople almost fell in 1400 - if it does, [FONT="]weirdly you might see Bayezid overconfident and thus wind up losing to Timur.)
The question is, till the Karaminids consolidate power, is there a country that can build up enough strength to keep the Karaminids honest if they end up taking all of Anatolia by, say, 1450? If so, the Karamanid Empire might not want to push into Europe and might be wiling to let European traders cross into Asia along the Silk Road.
Of course, if as noted France winds up allying with this group against Spain and the Austrians, then you could have the French trying to block Spanish traders which could have the Spanish seeking a Western route to Asia anyway.
If the Karamanids don't hold onto Egypt too strongly, it might be able to be a regional power in that area, which could mean an interesting dynamic between it, the Karamanid Empire, and Persia. If this blocks Karamanids from entering and takign Northern Africa, who gets it? The Egyptians? Perhaps. Or, could Europeans start trying to get land in Northern Africa centuries early? A desire for a military base in the Southern ports of the Mediterranean might cause it to becomea big battleground between Spain and France - maybe not as big as Italy bit bit enough.
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