Many worlds (by which I mean the Everett interpretation, not sure which you mean) is 100% deterministic. The impact that apparent world branching has to domain

Many worlds (by which I mean the Everett interpretation, not sure which you mean) is 100% deterministic. The impact that apparent world branching has to domain of the free will question is purely due to the "amplification effects" that a complex control system like our brain can have in reaction to something perceived as a "measurement" result. We cannot sense a superposition state directly. The moment we probe a particle, our instruments and us (the environment) becomes entangled with the observed particle. The instrument and later we the observers of the instrument are ourselves a quantum system with a well defined quantum stats, and a third observer not yet entangled with us can treat as still in a superposition state. The idea is that everything evolves according to the Schrodinger equation. The wave function never really collapses. The illusion of wave function collapse springs out of the way that a control system like a brain or a mechanical automaton processes it's inputs while being in an entangled state with the thing they observe and thus react to it's state differently in the different superimposed states. This difference becomes amplified. A control system like a brain is not necessary; just pure macroscopic environments are enough to diverge the apparent state of the systems so that it's useful to think in terms of "world splitting"; but it's just a useful fiction; very useful because that's all we'll ever witness. The amplification effect of control systems makes it easy to concoct extreme thought experiments. Let's imagine that spin up means you fire off a rocket and go to Mars and spin down means you stay put. All we did is that we managed to amplify the effect of this single superimposed state of one particle, into a macroscopic superposition of a rocket being on earth or on mars