  We use the IllustrisTNG (TNG) cosmological simulations to provide theoretical
expectations for the dark matter mass fractions (DMFs) and circular velocity
profiles of galaxies. TNG predicts flat circular velocity curves for $z = 0$
Milky Way (MW)-like galaxies beyond a few kpc from the galaxy centre, in better
agreement with observational constraints than its predecessor, Illustris. TNG
also predicts an enhancement of the dark matter mass within the 3D stellar
half-mass radius ($r_\mathrm{half}$; $M_\mathrm{200c} =
10^{10}-10^{13}\mathrm{M}_{\odot}$, $z \le2$) compared to its dark matter only
and Illustris counterparts. This enhancement leads TNG present-day galaxies to
be dominated by dark matter within their inner regions, with
$f_\mathrm{DM}(<r_\mathrm{half})\gtrsim0.5$ at all masses and with a minimum
for MW-mass galaxies. The 1$\sigma$ scatter is $\lesssim$ 10~per~cent at all
apertures, which is smaller than that inferred by some observational datasets,
e.g. 40 per cent from the SLUGGS survey. TNG agrees with the majority of the
observationally inferred values for elliptical galaxies once a consistent IMF
is adopted (Chabrier) and the DMFs are measured within the same apertures. The
DMFs measured within $r_\mathrm{half}$ increase towards lower redshifts: this
evolution is dominated by the increase in galaxy size with time. At $z\sim2$,
the DMF in disc-like TNG galaxies decreases with increasing galaxy mass, with
$f_\mathrm{DM}(<r_\mathrm{half}) \sim 0.10-0.65$ for $10^{10} \lesssim M_{\rm
stars}/\mathrm{M}_{\odot} \lesssim 10^{12}$, and are two times higher than if
TNG galaxies resided in Navarro-Frenk-White dark matter haloes unaffected by
baryonic physics. It remains to be properly assessed whether recent
observational estimates of the DMFs at $z\sim2$ rule out the contraction of the
dark matter haloes predicted by the TNG model.
