  We present a unified model for molecular core formation and evolution, based
on numerical simulations of converging, supersonic flows. Our model applies to
star formation in GMCs dominated by large-scale turbulence, and contains four
main stages: core building, core collapse, envelope infall, and late accretion.
During the building stage, cores form out of dense, post-shock gas, and become
increasingly centrally stratified as the mass grows over time. When the shock
radius defining the core boundary exceeds $R\approx 4 a (4\pi G
\rho_{mean})^{-1/2}$, where $a$ is the isothermal sound speed, a wave of
collapse propagates from the edge to the center. During the building and
collapse stages, density profiles can be fit by Bonnor-Ebert profiles with
temperature 1.2 - 2.9 times the true value. As found previously for initially
static equilibria, outside-in collapse leads to a Larson-Penston density
profile $\rho \approx 8.86 a^2/(4 \pi G r^2)$. The third stage, consisting of
an inside-out wave of gravitational rarefaction leading to $\rho\propto
r^{-3/2}$, $v\propto r^{-1/2}$, is also similar to that for initially-static
spheres, as originally described by Shu. We find that the collapse and infall
stages have comparable duration, $\sim t_{ff}$, consistent with estimates for
observed prestellar and protostellar (Class 0/I) cores. Core building takes
longer, but does not produce high-contrast objects until shortly before
collapse. The time to reach core collapse, and the core mass at collapse,
decrease with increasing inflow Mach number. For all cases the accretion rate
is $\gg a^3/G$ early on but sharply drops off; the final system mass depends on
the duration of late-stage accretion, set by large-scale conditions in a cloud.
