  (abridged) We present simulations of halo formation and evolution in scalar
field dark matter (SFDM) cosmologies in the Thomas-Fermi regime, aka
``SFDM-TF", where a strong repulsive 2-particle self-interaction (SI) is
included, being a valuable alternative to CDM, with the potential to resolve
its ``cusp-core" problem. In general, SFDM behaves like a quantum fluid.
Previous literature has presented two fluid approximations for SFDM-TF, as well
as simulations of halo formation. These results confirmed earlier expectations
and are generally in mutual agreement, but discrepancies were also reported.
Therefore, we perform dedicated 3D cosmological simulations for the SFDM-TF
model, applying both fluid approximations, as well as for CDM. Our results are
very well in accordance with previous works and extend upon them, in that we
can explain the reported discrepancies as a result of different simulation
setups. We find some interesting details: The evolution of both SFDM-TF and CDM
halos follows a 2-stage process. In the early stage, the density profile in the
center becomes close to a $(n=1.5)$-polytropic core, dominated by an
"effective" velocity-dispersion pressure $P_{\sigma}$ which is common to both
dark matter models. Consecutively, for CDM halos, the core transitions into a
central cusp. In SFDM-TF halos, the additional pressure $P_\text{SI}$ due to SI
determines the second stage of the evolution, where the central region follows
closely a $(n=1)$-polytropic core, embedded in a nearly isothermal envelope,
i.e. the outskirts are similar to CDM. We also encounter a new effect, namely a
late-time expansion of both polytropic core plus envelope, because the size of
the almost isothermal halo envelope is affected by the expansion of the
background universe. So, an initial primordial core of $\sim 100$ pc can evolve
into a larger core of $\gtrsim 1$ kpc, even without feedback from baryons.
