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Frederick VII of Denmark lack of legitime heir was the excuse for the Schleswig Wars. While the the conflict could still happen, whether the German Federation could or would intervene without this excuse is the greater question. As I see it, if the conflict still happens, we will likely see a the London conference end the war in 1849, in OTL they broke down over Denmark refusal to yield on "the principle of the indissoluble union with the Danish crown". Here this is irrelevant with a clear heir.

Could he get a heir? There's clear indication that he did father a illegitime child. So less him being a little less offensive, so that one of his two first royal wives do produce a child. Let say it's the first one Vilhelmine Marie of Denmark his cousin. They get a healthy son (*Christian IX) in 1836, and she decide to stay with him, maybe they get a son more, but after that they (she) decide to live separate from each others.

The 1st Schleswig War still start in 1848, Prussia still enter (more or less accidental), but the Hohenzollern are finding out that they on the side of the liberals, they as in OTL try to find a way out. The London Conference end with status quo (with Holstein as part of the German Confederation and Schleswig not) and recognise Frederik VII's son right to Schleswig-Holstein.

Without that there's no reason for Denmark to create the conflict which started the second war. But that means that Prussia lack a excuse for taking on Austria, but Bismarck clearly need that conflict to make Prussia a real power.

So he find a conflict (suggestions?) and the rest is history. Denmark stay outside like Netherlands did. After the war the North German Confederation is establish, but Mecklenburg, Lübeck and Hamburg stay outside (no reason to join*).

Do the French-Prussian War still happens? I see no reason for why not, maybe it's start over something different, but it's still going to happens, and it ends up like OTL.

So we have a German Empire which lack Mecklenburg, Hamburg, Lübeck and Schleswig-Holstein, it's around 5% of the empire's population.

What happens afterward?

*none of them was members of the Zollverein, and Denmark clearly didn't want to conquer them, so no need for a military alliance, Lübeck may want to join, but I doubt Prussia want it as a enclave.
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