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In TTL the "Trent Affair" really blows up and war breaks out between the US and UK. The US looks for allies and finds them in Russia and Prussia. Russia sees the US as a counterweight to GB and Prussia is among the weakest of the Great Powers at this time (Although strengthening quickly) and looking for allies in case war breaks out. Russia continues its reforms in this TL partly due to American influence. The Prussians hook up with Austria-Hungry as well for the same reasons as OTL while the French and British align with Spain due to the worrying about the Russian-Prussian-AH-US alliance. The Great War breaks out in 1910 over any number of reasons. The sides are UK-France-Spain-CSA vs US-Russia-Prussia-AH. I think the US and CS would cancel most of their participation but the US would be able to send at least some of its fleet on raids. Due to distance I think both the US and UK would be mostly raiding each others fleets rather than doing knock out drag down fights.