  The birth process of circumstellar disks remains poorly constrained due to
observational and numerical challenges. Recent numerical works have shown that
the small-scale physics, often wrapped into a sub-grid model, play a crucial
role in disk formation and evolution. This calls for a combined approach in
which both the protostar and circumstellar disk are studied in concert. We aim
to elucidate the small scale physics and constrain sub-grid parameters commonly
chosen in the literature by resolving the star-disk interaction. We carry out a
set of very high resolution 3D radiative-hydrodynamics simulations that
self-consistently describe the collapse of a turbulent dense molecular cloud
core to stellar densities. We study the birth of the protostar, the
circumstellar disk, and its early evolution (< 6 yr after protostellar
formation). Following the second gravitational collapse, the nascent protostar
quickly reaches breakup velocity and sheds its surface material, thus forming a
hot ($\sim 10^{3}$ K), dense, and highly flared circumstellar disk. The
protostar is embedded within the disk, such that material can flow without
crossing any shock fronts. The circumstellar disk mass quickly exceeds that of
the protostar, and its kinematics are dominated by self-gravity. Accretion onto
the disk is highly anisotropic, and accretion onto the protostar mainly occurs
through material that slides on the disk surface. The polar mass flux is
negligible in comparison. The radiative behavior also displays a strong
anisotropy, as the polar accretion shock is shown to be supercritical whereas
its equatorial counterpart is subcritical. We also find a remarkable
convergence of our results with respect to initial conditions. These results
reveal the structure and kinematics in the smallest spatial scales relevant to
protostellar and circumstellar disk evolution.
