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We generalize the construction of time-reversal symmetry-breakingtriple-component semimetals, transforming under the pseudospin-1representation, to arbitrary (anti-)monopole charge $2 n$, with $n=1,2,3$ inthe crystalline environment. The quasiparticle spectra of such systems arecomposed of two dispersing bands with pseudospin projections $m_s=\pm 1$ andenergy dispersions $E_{\bf k}=\pm \sqrt{ \alpha^2_n k^{2n}_\perp +v^2_zk^2_z}$, where $k_\perp=\sqrt{k^2_x+k^2_y}$, and one completely flat band atzero energy with $m_s=0$. We construct simple tight-binding models for suchspin-1 excitations on a cubic lattice and address the symmetries of thegeneralized triple-component Hamiltonian. In accordance to the bulk-boundarycorrespondence, triple-component semimetals support $2 n$ branches oftopological Fermi arc surface states and also accommodate a \emph{large}anomalous Hall conductivity (in the $xy$ plane), given by $\sigma^{\rm 3D}_{xy}\propto 2 n \times$ the separation of the triple-component nodes (in units of$e^2/h$). Furthermore, we compute the longitudinal magnetoconductivity, planarHall conductivity, and magneto thermal conductivity in these systems, whichincrease as $B^2$ for sufficiently weak magnetic fields ($B$) due to thenontrivial Berry curvature in the medium. A generalization of our constructionto arbitrary integer spin systems is also highlighted.

Generalized Triple-Component Fermions: Lattice Model, Fermi arcs, and Anomalous Transport