The aim of this ambitious research project is to produce the most realistic computer simulations of the assembly of gaseous protoplanetary accretion discs, and to understand which of their traits are inherited from and/or affected by their direct interstellar context. Owing to ground-breaking instruments such as VLT/Sphere or the ALMA telescope array, we now have a first extensive census of disk populations. Moving beyond the core characterisation of relatively isolated disks in the calm Class II stage, the time has come to shift the focus towards the wider context of these systems, that is, the actively star-forming stellar associations, such as the archetypal Taurus, Orion or Lupus regions. Stellar ages of disks with substructure of (likely) planetary origin point to the fact that planet formation is not merely an ubiquitous process, but figuratively speaking happens within the blink of an eye. This mandates to abandon the assumption of the disk as a quiescent entity detached from its surroundings, and instead place it in the context of a collapsing cloud core. Key aspects here are i) the external UV radiation field that can drive powerful photochemical reactions on the surface, ii) perturbations from stellar flybys, iii) gas self-gravity, and iv) magnetic field lines that are self-consistently anchored in the local interstellar medium (ISM); the latter aspect requiring adaptive-mesh technology, provided by the NIRVANA III code, co-developed by the applicant. At the same time, the early appearance of planets poses questions about the solid constituents potentially being inherited from the ISM and “primed” during the protostellar precursor phase. Finally, with the pivotal exchange of angular momentum during the collapse regulated by non-ideal MHD effects, the evolution of microphysical coefficients (i.e., through an ionisation chemistry with recombination on small grains) needs to be followed through the collapse phase, accounting for dust growth by coagulation.