  Scalar Field Dark Matter (SFDM) comprised of ultralight bosons has attracted
great interest as an alternative to standard, collisionless Cold Dark Matter
(CDM) because of its novel structure-formation dynamics, described by the
coupled Schr\"odinger-Poisson equations. In the free-field ("fuzzy") limit of
SFDM (FDM), structure is inhibited below the de Broglie wavelength, but
resembles CDM on larger scales. Virialized haloes have "solitonic" cores of
radius $\sim\lambda_\text{deB}$, surrounded by CDM-like envelopes. When a
strong enough repulsive self-interaction (SI) is also present, structure can be
inhibited below a second length scale, $\lambda_\text{SI}$, with
$\lambda_\text{SI}> \lambda_\text{deB}$ -- called the Thomas-Fermi (TF) regime.
FDM dynamics differs from CDM because of quantum pressure, and SFDM-TF differs
further by adding SI pressure. In the small-$\lambda_\text{deB}$ limit,
however, we can model all three by fluid conservation equations for a
compressible, $\gamma=5/3$ ideal gas, with ideal gas pressure sourced by
internal velocity dispersion and, for the TF regime, an added SI pressure,
$P_\text{SI}\propto \rho^2$. We use these fluid equations to simulate halo
formation from gravitational collapse in 1D, spherical symmetry, demonstrating
for the first time that SFDM-TF haloes form with cores the size of
$R_\text{TF}$, the radius of an SI-pressure-supported $(n=1)$-polytrope,
surrounded by CDM-like envelopes. In comparison with rotation curves of dwarf
galaxies in the local Universe, SFDM-TF haloes pass the ["too-big-to-fail" +
"cusp-core"]-test if $R_\text{TF}\gtrsim 1$ kpc.
