at a proper theoretical description of early protostar evolution. In particular, recent studies show that the mass-infall rate during the protostellar phase is quite sensitive to the core radial density profile at the onset of dynamical collapse. When the initial density profile is flatter than $\rho \propto r^{-2} $ near core center, then the mass-infall rate is expected to feature a strong initial peak, followed by a sharp decline, at the beginning of the main accretion phase (e.g. Foster & Chevalier 1993; Henriksen, André, & Bontemps 1997). The outer core density profile also plays a fundamental role by determining whether the mass reservoir ultimately available for star formation is effectively finite or infinite. If the radial density profile approaches $\rho \propto r^{-2} $ up to large radii as in the standard paradigm of isolated star formation (Shu et al. 1987), then the mass reservoir is much larger than a typical stellar mass and feedback processes such as outflow/inflow interactions (e.g. Velusamy & Langer 1998) must eventually stop accretion onto the central protostar. On the other hand, if the initial core density profile becomes steeper than $\rho \propto r^{-3}$ beyond some finite radius, then the mass reservoir is limited and the 