There are certainly hundreds of theories as to who, ultimately, decided the fate of the Jews, and most of them don't include Hitler at all. Certainly we know that the holocaust was their their original objective. The "Jewish Question" had a few possible solutions - like Madagascar - that simply couldn't work, and others that they started to implement, but there were obvious flaws - such as sending them to Eastern Europe. This proved a problem when they... took over Eastern Europe and realised, "*******s, here are the Jews again." The holocaust - that is, the destruction of the Jewish people in massive numbers - was more out of lack of alternatives and panic.
Indeed, we can see the numbers of Jews dying, month by month, altering dependent on the success of the German war effort. When it looked like Germany was going to take over Russia, less Jews were killed when it became more likely that they could just shove them the other side of the Urals. As they got beaten back, "production" increased, partly due to the aforementioned lack of alternative, but also so that, were their camps over run (many of which, of course, were not actually in Germany), there would be no jews to tell the tale...
There's a lot of debate about who actually gave the order. Certainly, no direct order from Hitler has ever been discovered or reasonably attested to, though perhaps it was just too secretive. There's the issue of the Wanssee conference, where a bunch of people who weren't Hitler decided the fate of the Jews (though the outcome of the meeting - ie, slaughter - was generally believe to be pre-conceived and so possibly from someone higher up). Some blame the church for not intervening, some the the SA and SS, etc etc.
But the idea of Hitler being in charge of it all is certainly not definitive in any way. That said, he was notoriously unofficial in his orders, so it's possible he was in charge, just without the paperwork to back it up, though if this is true, we'll probably never know. And this is only relating to the holocaust, but much of Germany's actions in this era are marked by the same questions and uncertainty of power and authority.
Imo.