The alt-path focuses are a bit janky, because how the AI implements them seems to be affected by what country you are playing as. For example, I did a "pacifist" Monarchist Germany run (get the Kaiser back and then only engage in defensive wars and make no territorial claims) and the UK AI never picked whether or not to do "Steady as She Goes" or "A Change in Course". Because I, as Germany, did not do either of the main Monarchist focus paths ("Focus on the True Enemy" or "Expatriate the Communists") the AI couldn't chose where to go on it's tree, because the AI is coded to respond to German player actions. France went communist (they usually do prior to 1.9 because of how the AI handles the early-game labor strikes) but the UK was paralyzed. They didn't even choose to Reinforce or Dismantle the Empire because I was ignoring 75% of my focus tree. On any other playthrough, the UK has decided which way to go on it's tree by the latter half of 1937 at the latest.
When the UK does go alt-history, I find it does a better job of it than it used to. I remember in 1.7 (I'm playing in 1.8 currently) the UK never once managed to go fascist without a civil war. Now I can't remember the last time I saw a British civil war. It still has issues going communist, where it will concede to the unions, decolonize by 1940, then hover at 45% communist support until 1948 and never seal the deal. I've seen them complete the communist focus path before, but it's still a rare occurrence. I think it may have something to do with whether or not the USSR is still in existence, because the two times I've seen it happen, the Russians were sitting pretty with nobody going to war with them. Most every other game, the UK stops adding communist political support to it's politics pie as soon as the USSR gets annexed.
As for other countries, I've only seen the US do any of it's alt-history paths when I have specifically told the AI to do them, or one time when they went communist on their own (though I think Trotsky was boosting communism there for a while). I've never seen the AI US do alt-history without being told to, or without having the player force the issue through political manipulation.
Hungary tends to do Rome Protocols (which is technically alt-history, even though it is still fascist) fairly often, especially if Germany goes monarchist. Second most popular is the restoration of Austria-Hungary. I've only seen them go down the communist path if I've made the AI do it, but I've never seen Hungary actually flip governments. The communist tree does not provide any actual communist political support, which means Hungary has to appoint a communist advisor to get any. The AI seems to be coded to never take the communist advisor, so the country never progresses past the first communist focus. Which is good, because the Hungarian communist branch is terrible and nobody should ever take it.
I usually run mods for Poland and Russia, but when achievement farming I've seen Russia go for Trotsky all of once. Poland will try to form it's own faction if Germany takes long enough on it's tree to get around to making territorial demands. Sometimes it will even go fascist, though I've seen it go communist once (and then get eaten by Germany immediately after, so no real change to the gameplay experience there).
France's actions are dependent on the UK, mostly. If the UK does "A Change in Course", France goes for "Little Entente" around 90% of the time. Even if they don't, Czechoslovakia usually does, and I've only seen France refuse to join the faction once (and then get eaten by Germany immediately after, so no real change to the gameplay experience there, either). France, even if it selects democratic options from its tree, can wind up communist because of how it handles the various strikes. It's not surprising to me to see France join the Allies in 1939 and be the French Commune by 1942. I don't have the new tree in LaR, so I can't speak to how often it may or may not go Monarchist.
I've never seen Czechoslovakia effectively switch governments. I've seen it try a few times, but considering how difficult it is to change ideologies as a Czech player, the AI has no hope of flipping before Germany eats it. The only time I've seen fascist Czechoslovakia is when fascist Poland puppetted them.
Italy, surprisingly enough, goes fascist no matter what happens. I wonder why that is. You never see them go democratic or communist. Can't figure out why, for the life of me...
Romania is such a wild card I can't predict them. If you aren't playing Germany (and thus can't ensure their politics through the "Align Romania" focus) Romania will tend to start neutral, go Monarchist, and then has an even chance of ending up as a democracy, a fascist dictatorship, or staying monarchist. I've only seen them go communist after the USSR puppetted them.
Japan seems to go Monarchist fairly often. I'm not sure of the exact % chances for the various branches of it's tree (I'm not code-literate enough to figure it out) but it feels like 40% fascist, 40% monarchist, 10% communist, 10% democracy, with a strong weight on fascist if you are playing China or Manchukuo.
The Commonwealth nations seem to be dependent on the UK as well. If the UK goes historical, they tend to do the same. India sometimes throws a wrench into it by trying to break free via civil war, but generally everybody plays ball if the UK stays the course. If the Dominions break with the UK, Canada often changes ideology (fascist seems more common for them than communist, probably because the Devs like that memey picture of fascist Canada's leader) but if the UK decolonizes, Canada tends to stay a democracy (as the new leader of the Allies its kind of expected). I've never seen India succeed in an independence war, though. They try to break away, but they time it terribly and end up having to fight the whole of the Allies, instead of just the Raj (WT monitoring as India is super important if you want to break away and the AI is bad at it) and so they end up getting stepped on pretty hard.
Yugoslavia tends to follow the historical path more or less. I rarely see them go communist on their own initiative, and their fascist branch and their historical branch have so much overlap that unless their political pie turns yellow, it's hard to tell if they've gone alt-history or not.
China determines it's actions based on what Japan does, if it knows what's good for it. If it sees Japan go monarchist (or any not-fascist path) it tends to get the knives out and go after Comm China and the warlords. Usually at the same time. The only times China switches ideology is, again, when someone turns them into a puppet. China doesn't have much of an alt-history path to begin with... its basically "make friends and punch Japan" or "ignore Japan and punch everyone else". I've seen China pick the "punch everyone else" path while Japan went fascist once or twice. Predictably, it results in Japan owning everything. Usually, though, the AI is smart enough to tie it's actions to Japan's decision to stay fascist or not.
Did I miss anyone?
Also: playing in 1.8 with no LaR, so YMMV.
