  Using the JVLA, we explored the Galactic center (GC) with a resolution of
0.05" at 33.0 and 44.6 GHz. We detected 64 hyper-compact radio sources (HCRs)
in the central parsec. The dense group of HCRs can be divided into three
spectral types: 38 steep-spectrum ($\alpha\le-0.5$) sources; 10 flat-spectrum
($-0.5<\alpha\le0.2$) sources; and 17 inverted-spectrum sources having
$\alpha>0.2$, assuming $S\propto\nu^\alpha$. The steep-spectrum HCRs are likely
represent a population of massive stellar remnants associated with nonthermal
compact radio sources powered by neutron stars and stellar black holes. The
surface-density distribution of the HCRs as function of radial distance ($R$)
from Sgr~A* can be described as a steep power-law $\Sigma (R) \propto
R^{-\Gamma}$, with $\Gamma=1.6\pm0.2$, along with presence of a localized
order-of-magnitude enhancement in the range 0.1-0.3 pc. The steeper profile of
the HCRs relative to that of the central cluster might result from the
concentration massive stellar remnants by mass segregation at the GC. The GC
magnetar SGR~J1745-2900 belongs to the inverted-spectrum sub-sample. We find
that two spectral components present in the averaged radio spectrum of
SGR~J1745-2900, separated at $\nu\sim30$ GHz. The centimeter-component is
fitted to a power-law with $\alpha_{cm}=-1.5\pm0.6$. The enhanced
millimeter-component shows a rising spectrum $\alpha_{mm}=1.1\pm0.2$. Based on
the ALMA observations at 225 GHz, we find that the GC magnetar is highly
variable on a day-to-day time scale, showing variations up to a factor of 6.
Further JVLA and ALMA observations of the variability, spectrum, and
polarization of the HCRs are critical for determining whether they are
associated with stellar remnants.
