HERE WE PROPOSE UNDERTAKING A SET OF THREE-DIMENSIONAL SIMULATIONS WHICH OVERCOME THIS.LIMITATION AND ARE AIMED AT PROVIDING ROBUST ANSWERS TO THE FOUNDATIONAL QUESTIONS IN MAGNETIZED.STELLAR ACCRETION. HOW DO NEUTRON STARS PRODUCE RELATIVISTIC JETS (SECTION 1.2.1)? WHAT.IS THE NATURE OF THE DISK{MAGNETOSPHERE INTERACTION AND NEUTRON-STAR SPIN-UP AND -DOWN.(SECTIONS 1.2.2 AND 3.1)? WHAT EXPLAINS TRANSITIONAL MILLISECOND PULSARS' STRANGE BEHAVIOR.(SECTIONS 1.2.3 AND 3.2)? WHAT CAN WE LEARN FROM THE DI.ERENCES AND SIMILARITIES BETWEEN.ACCRETING NEUTRON STARS AND BLACK HOLES