  We study the extent to which a three-dimensional dispersing Periodic Anderson
Model (PAM) can explain the emergence of novel superconductivity in the
Infinite-Layer Nickelate compounds. By going beyond frequently used 2D models,
the 3D dispersing PAM allows us to incorporate effects of finite out-of-plane
hopping and orbital hybridization in describing these systems. Using an
unbiased functional Renormalization Group (fRG) approach, we show that
$d_{x^2-y^2}$ superconductivity arises in a series of 3D {\it {ab-initio}}
models of the Nickelates ({\it {e.g.}}$\mathrm{RNiO_2}$), where R is a rare
earth element. We the study the impact of going beyond the Ni-d orbital by
including the R-$d_{z^2}$ and the interstitial-$s$ as hybridizing conducting
bands. We explore the dependence of the models on key parameters, including the
local Hubbard coupling, doping and temperature. We find the hybridization with
the interstitial-$s$ band driving a 3D $d_{z^2-r^2}$-type superconductivity
while out of plane hopping primarily enhances an $s$-wave superconducting
order.
