AHC: Create the largest possible Ottoman Empire

That depends on how stable you are willing to allow them to be.

Theoretically, the Ottomans could conquer Iran. It will be easier if you keep Iran mostly Sunni, rather than going Shia.

They could have more protectorates, such as Morocco, Aceh, Kanem-Bornu etc.
 
Here's a relatively simple challenge. How much can you wank the Ottomans, and how large can you make them in the process?
That depends on how stable you are willing to allow them to be.

Theoretically, the Ottomans could conquer Iran. It will be easier if you keep Iran mostly Sunni, rather than going Shia.

They could have more protectorates, such as Morocco, Aceh, Kanem-Bornu etc.
Add maybe a sucessful conquest of Austria and Italy? that is the largest i could imagine
 
I think the Ottomans would be best served in gaining sheer land by ignoring Hungary once they dislodge them north of the Danube plus establish either vassals or military provinces akin to OTL's Bosnia Elayet in Transylvania/The Danubian Provinces, Vojvodina, Bosnia + Slavonia, Croatia Proper and the Crimea leaving them in undisputed control of the Danube and the Sava. Leaving those areas as military provinces while leaving a weak but not dependent Hungary north of the Danube makes the Ottomans' European flank more secure. And they can ideally mirror OTL Bosnia's religious history in some form giving the Ottomans more Muslims in the Balkans should they eventually lose control of these territories but keep their core in the Southern Balkans.

From there the Ottomans would IMO be best served in securing the title of Caliphate as decisively as possible. This means annexing Persia and the Gulf, establishing tributaries in Yemen(the mountainous highlands aren't worth fighting for IMO), northern Sudan, East Africa/Madagascar, and tightening their reigns over North Africa. Ideal strategic targets to gun for are Malta, Hormuz, and Zanzibar. To go along with this naval initiative would be direct attempts to stunt European adventures east of the Cape; stunt but not shut down. This gives the Ottomans some amount of leeway in playing off their military adventures in the Indian Ocean as pious Muslim initiatives while building up to an eventual ideology of pan-Islamism later on, whereas if they'd shut them down completely there'd be zero inkling of truth to this idea.

To meet the OP's challenge, you absolutely have to have the Ottomans take control of Australia for the sheer amounts of land that it adds to their sum total. And to go along with these a loose suzerainty over key Muslim regions under European siege, such as Aceh, the southern Philippines, Java, Malacca, etc. Because this theoretical Ottoman state focused their resources on the Indian Ocean and the Mediterranean instead of Central European adventures, let's say that they, not the Dutch are the ones to tear Portugal's empire asunder. This is the window where you can have the Ottomans come into control of strategic locations such as Hormuz, Muscat, Zanzibar, and Malacca/Singapore in some sort of analogue war during the Dutch War of Independence where the Ottomans come in like vultures. This is also where they could hop into seize the Philippines and Malta. If you really want to go for the gold medal, Gibraltar to unleash Maghrebi piracy on the Caribbean and Sevilla.

Fastforward a couple hundred years to the start of the industrial revolution and the Ottomans are in about the same position of dominance in the Indian Ocean that Britain found itself in at the end of the Napoleonic Wars except there's no one to give colonies back to. Definitely not leading the charge to industrialization but their stronger commercial links and greater involvement in trade and shipping means that they're going to adapt FAR better to industrialization and can hold their own. Fast forward another century to some ATL Scramble and the Ottomans are the 800 pound gorilla in the room as they've got East Africa, North Africa, and the Sahara on lockdown and have the Sahelian Muslim states in their pocket. While European states are fighting over mostly non-Muslim territories such as the West African coast and the Congo, the Ottomans' soft vassalage system used in Indonesia and later the Pacific has most of Europe by the balls. Between control of the Suez Canal, the Straights of Malacca, and almost all of the Indian Ocean's trade routes no European state that values trade with Asia is willing to push too aggressively on Ottoman vassals along the Niger River and the Sahelian band. Everything north between the Maghreb and the Sahel is indisputably Ottoman, no other power has any influence or means to push for land here.

Fast forward 20 years and the monopoly on oil, the demographics, and the pan-Islamist ideology being blasted by mass media has turned the Ottomans into a superpower bordering on a hyperpower in the Old World(presuming that a USA analogue arises and holds strong over the New World, otherwise nope, the Ottomans are an outright hyperpower).

This is about the theoretical peak for Ottoman expansion IMO. Exactly what lands they have or to what extent it's 'Ottoman', eh, that's all for someone more invested than me to debate. What I think the best bet for this to transpire would be an early shift in priorities from Europe to the Middle East for the Ottomans. Avoiding the Ottoman Interregnum is a good start and gives them a 50 year headstart, but I prefer a more ambitious hypothetical, where the Ottomans goad the Timurids into the same war as OTL but do so purposefully and rout them/slay Timur. This leaves an incredible power vacuum in the Middle East that they can ride all the way to Persia(IMO). This shifts almost all Ottoman attention away from the Balkans and butterflies the rise of Shia Islam in Iran. The Ottomans will be preoccupied with these adventures in the Middle East for close to the same amount of time as they spent in the interregnum if not longer and will come out with a radically altered set of priorities. This may even lead to the Persification of the Ottoman state and see them viewed by Europe as the second coming of the Achemaenid Persian Empire. And with that shift in character comes the permanent shifting of mentality and goals from a successor of Rome to a successor of Persia or even a successor of both. But whatever minimizes the attractiveness of marching into Vienna and defeating the HRE or marching into the Papacy and subjugating more Roman institutions that are more trouble than they're worth, the better.
 
Ottomans conquering Iran + Indian-Ocean-focused-Ottomans dovetail well, but there'd have to be some reason why adding Persia's rather small bit of coast makes the Ottomans more focused on the Indian Ocean when they already had Egypt, the Hejaz, the Arab side of the Gulf Coast, and Yemen. Maybe the Ottoman authorities in Iran link up with Oman, and the Indian Ocean ventures are explicit collaborations between the two with the initial aim of chasing Portugal away from Africa, and later...
 
Ottomans conquering Iran + Indian-Ocean-focused-Ottomans dovetail well, but there'd have to be some reason why adding Persia's rather small bit of coast makes the Ottomans more focused on the Indian Ocean when they already had Egypt, the Hejaz, the Arab side of the Gulf Coast, and Yemen. Maybe the Ottoman authorities in Iran link up with Oman, and the Indian Ocean ventures are explicit collaborations between the two with the initial aim of chasing Portugal away from Africa, and later...

That was more or less my train of thought. If the Ottomans are already established(as well as preoccupied) with solidifying control over Persia then when the Portuguese come knocking into the Indian Ocean and set up shop in places such as Muscat and Hormuz, the Ottomans more fully commit to the Indian Ocean than OTL and successfully dismantle the Portuguese feitoria system in the process, more or less co-opting it. OTL they already saw Portugal's adventures as a threat. With them setting up shop in Hormuz as an immediate neighbor, kicking Portugal's ass goes from a nice goal to a priority, especially if they've got armies and resources already invested into pacifying the region. It's far easier to commit resources to the Indian Ocean if you're already focused on subjugating Iraq + Iran.

Thinking on it a bit further, Eastern Anatolia would be a tremendous trouble spot for the Ottomans for decades upon decades with on and off flareups as in OTL, but with the conquest of even more Shiite Turkmen than OTL, they'll have to dedicate even more resources to this. This both helps in centering their focus on their geographical center(Upper Mesopotamia/al-Jazira) and detracts them from getting too ambitious in the Balkans. A net positive when trying to work out a scenario that leads the Ottomans to the Indian Ocean. It even makes you wonder if the capital would still be in Constantinople longterm instead of Baghdad or something more Persian-inspired like resurrecting an old Persian capital like Persepolis or Ctesiphon with how Constantinople will be shifting from the center of the Empire to a periphery. If they overrun Persia before returning to conquer Constantinople then the impetus is there to set up shop in their new crown jewel and the whole Kayser-i-Rum schtick might never come up; Constantinople's conquest shifts from being the confirmation of their replacement of the Eastern Romans to being an affirmation of either walking in the shoes of the old Achaemenid Empire or fulfilling a historical Muslim aspiration.

Without their political center in Constantinople these alt-Ottomans would have far less resources to put into domineering the North African states but there's a good chance they may come to the Ottomans anyways once they're in control of all of the Levant, Egypt, Anatolia and Persia due to a need for allies against the Iberians. Maybe slower than OTL but the increased maritime focus compared to OTL's fixation on Vienna makes a strong case for a similar trajectory for North Africa's political domination by the Ottomans.
 
It might be important to note, that the ottoman state was by its nature, an European state... Especially after the disaster of 1402. Their interests are more towards Europe than to the Middle East. In fact, much of the larger woes that befell her, were in the Mid East. Long drawn conflicts and economic drains were found in Iraq, Iran, Egypt and so forth. The conception of caliphate further emboldened the Ottomans into wars with varied dangerous foes in unfamiliar lands, namely the Safavids. Their caliphate title, also harmed their relations with the Mughal empire, a possible grand ally.
 
And the Italian states are much weaker. Venice is still recovering from choggia and the plague. Milan is about to collapse. Thr Church is still in schism. Sicily and Aragon are about to undergo a succession crisis. The Hundred Years war is only halfway through. The Hussite Wars are about to distract Hungary-Bohemia and Poland and Germany. If the Ottomans play their cards right and exploit Europes internal divisions they could be at the Alps by the 1440s.
Well, aside from just the western expansion, the Ottomans might have less trouble coming from the east in the long term. Without Timur, the Persian region's remains disunited in the wake of Ilkhanate collapse for at least a good while longer (plus, no Turkomen to revolt from). Without an Iranian power like the Safavids to check Ottoman eastward expansion and the constant expenditures of the Ottoman-Safavid wars, Ottoman dominance over the Middle East is far more secure and its borders perhaps stretching over the Zagros, no?
 
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