The ability of Axis states to impose conditions of the handover of Jews to the Nazis was dependent upon their "negotiating" position. The position of most was basically "foreign" Jews are yours but "our" Jews we will deal with. This dealing might have been almost as bad as what the Germans did or completely benign, such as Finland. In a Nazi victory scenario, the smaller Axis partners have very little negotiating power as now the Reich can decide to literally crush any state that does not comply. Sooner or later the smaller states will have to comply and load all the Jews on trains. In some places, their escape to some other haven may be facilitated, but that assumes there is someplace they can get to that will accept them even temporarily. Even neutrals like Sweden, Switzerland, Turkey, and Spain will be pressured both to give up escapees (escaped criminals). I expect sooner or later some neutrals who are basically surrounded by Nazi territory will be told the price of their continued independence is to give up "their" Jews. Hopefully since that sort of pressure would take time to build, the Jews there would have a chance at escaping out of reach.
With a vast host of Slavs to exploit as expendable slaves, there is no need for Jewish labor and the Jews will be sent to extermination camps for rapid processing. No doubt the Nazis will press the rest of the countries in the world to deport Jews to them, but I doubt they will make much headway - very few governments would be willing to deport their citizens, even Jews, to be exterminated even given that the locals get to confiscated everything the Jews own.
Getting in a war with the USA and the British Empire that remains free after this war, simply to kill the Jews, is not going to happen. Conquering the USA and eliminating the threat, with the happy side effect of Jewish extermination, sure. Making that happen especially in a world with nukes...
The bottom line is that however much the Axis small boys don't like giving up locals for death, given a choice between remaining relatively independent or not, the choice is obvious. The same would apply to vulnerable neutrals.
With a vast host of Slavs to exploit as expendable slaves, there is no need for Jewish labor and the Jews will be sent to extermination camps for rapid processing. No doubt the Nazis will press the rest of the countries in the world to deport Jews to them, but I doubt they will make much headway - very few governments would be willing to deport their citizens, even Jews, to be exterminated even given that the locals get to confiscated everything the Jews own.
Getting in a war with the USA and the British Empire that remains free after this war, simply to kill the Jews, is not going to happen. Conquering the USA and eliminating the threat, with the happy side effect of Jewish extermination, sure. Making that happen especially in a world with nukes...
The bottom line is that however much the Axis small boys don't like giving up locals for death, given a choice between remaining relatively independent or not, the choice is obvious. The same would apply to vulnerable neutrals.