A relatively popular alternate history Scenario concerns the possibility of Zhang He's voyages continuing to enjoy official backing after the death of the Yongle emperor.
For a variety of reasons, I tend to believe that if they had continued in the same format as OTL, the effect would not be very profound. The voyages were massively expensive and failed to produce either a profit or territorial gains.
Having a massive fleet with tens of thousands of personnel and massive armamanets sail the ocean blue may have been impressive (and I guess that was the point) but it's no way to run a profitable or self sustaining buisness.
The Europeans, and Latter Ming and Japanese Wokous, did it the right way. combine piracy, conquest, and legitimate trade, and only invest in sufficient ships and men to get the job done. The Europeans combined that with limited liability companies, a growing edge in technology and millitary techniques, a missionary zeal, and an incredibly high degree of loyalty and identification with the home countries to get the colonial ball rolling.
There is nothing in the Early Ming cultural make up that can equal that.
On the other hand, the voyages not only drained Ming coffers, which presumably had some effect on the adventure in Vietnam and the failure to sustain the subjugation of Manchuria, it also created a backlash at court which, at least for a time, destroyed China's naval industries, cut off overseas Chinese from the mother country, abandoned the coastlines to the Wokous, and discouraged the rudimentary private trading concerns of southern China.
So what if the Yongle emperor never sends Zheng He off on the voyages in the first place? What if he instead tasks him, together with his counterpart Yishiwa, to subdue the wild Jurchens on the Amur, and gives him all the resources which were expended on the treasure voyages?
I see a number of outcomes, some plausible, some not so much:
1. Manchuria, unlike Mongolia could be held down and colonized with the Chinese agricultural package. If the Ming made a real effort at it, before the dynasty lost it's vigor, then if and when they fall (might not with less Malthusian pressure and grain supplies from Manchuria) they are more likely to be replaced by a Manchurian based Han warlord than by a dynasty which self identifies and is identified by it's subjects as non "chinese".
2. Northeast Asia, unlike South East Asia, holds a major commodity which proved both immenesly profitable for Russian colonists to sell to China OTL, and whose pursuit encourages further naval exploration. Furs. And perhaps Fish. The stocks of both tend to be easily depleted unless under strict management but the bay of Okhotsk and Kamachatka are not much of a barrier to exploration and setting up trading posts. If the Imperial government makes Fur trading a government monopoly (as the Tsars did), that's a major source of income, and an incentive to sponser expeditions further up the coast.
3. The currents off Kamchatka are not very condusive to crossing the Bering strait. But storms do occur and if land is sighted or a ship is blown off course all the way to the American continent, The Chinese might eventually wise up to how the North Pacific Gyre operates and set up trading post in the New world, though they would probably never head far enough south to meet, let alone prempt the Europeans. Their germs and horses might though.
4. No backlash to Zheng He means that Overseas Chinese communities and trading links can continue to develop organically and gradually. That means greater cultural and economic presence in Indochina and Indonesia.
5. And that, in turn, means greater incentive by the Ming to conquer or vassilize those polities- though Vietnamese resistance has traditionally turned China off to that Idea, it is not incoceivable for Some enterprising Ming emperor to hit on a viable and self sustaining imperial model which taxes vassal states more than occupying them consumes. The Colonization of Taiwan might occur earlier. Even the philipines may become the target of official or semi-oficial colonization.
6. The Wokou era will have a harder time getting started. And if Hideyoshi does invade Korea it's quite likely to end much sooner with a real Ming fleet around.
7. If the Ming do have overseas interests, and these come into conflict with those of the Portugese and the Dutch, an attempt at modernization, rather than withdrawal, might be mad during the 16th century.
So let's assume the Yongle emperor offs his nephew and sees no reason to send Zheng He on a wild goose chase across the Indian ocean. Nor does he see any reason to move his capital to Beijing, with the officials in Nanking more accepting of his rule. Instead, Zhang he is sent back to over see Beijing and Manchuria, where he spends his time hammering the Jurchen into submission and planting millitary colonies along the Amur.
Which of the above possibilities seem plausible? As an additional twist assume the Yongle emperor sees no need to restore the Tranh to power in Dai Viet, at least not right away, given his own greater legitimacy.