  Given a $k$-uniform hypergraph $G$ with vertex set $[n]$ and edge set $E(G)$,
the ABC tensor $\mathcal{ABC}(G)$ of $G$ is the $k$-order $n$-dimensional
tensor with \[
  \mathcal{ABC}(G)_{i_1, \dots, i_k}=
  \begin{cases}
  \dfrac{1}{(k-1)!}\sqrt[k]{\dfrac{\sum_{i\in e}d_{i}-k}{\prod_{i\in e}d_{i}}}
& \mbox{if $e\in E(G)$}
  0 & \mbox{otherwise} \end{cases} \] for $i_j\in [n]$ with $j\in [k]$, where
$d_i$ is the degree of vertex $i$ in $G$. The ABC spectral radius of a uniform
hypergraph is the spectral radius of its ABC tensor. We give tight lower and
upper bounds for the ABC spectra radius, and determine the maximum ABC spectral
radii of uniform hypertrees, uniform non-hyperstar hypertrees and uniform
non-power hypertrees of given size, as well as the maximum ABC spectral radii
of unicyclic uniform hypergraphs and linear unicyclic uniform hypergraphs of
given size, respectively. We also characterize those uniform hypergraphs for
which the maxima for the ABC spectral radii are actually attained in all cases.
