  We analyze the structure of the surface states and Fermi arcs of Weyl
semimetals as a function of the boundary conditions parameterizing the
Hamiltonian self-adjoint extensions of a minimal model with two Weyl points.
These boundary conditions determine both the pseudospin polarization of the
system on the surface and the shape of the associated Fermi arcs. We
analytically derive the expectation values of the density profile of the
surface current, we evaluate the anomalous Hall conductivity as a function of
temperature and chemical potential and we discuss the surface current
correlation functions and their contribution to the thermal noise. Based on a
lattice variant of the model, we numerically study the surface states at zero
temperature and we show that their polarization and, consequently, their
transport properties, can be varied by suitable Zeeman terms localized on the
surface. We also provide an estimate of the bulk conductance of the system
based on the Landauer-B\"uttiker approach. Finally, we analyze the surface
anomalous thermal Hall conductivity and we show that the boundary properties
lead to a correction of the expected universal thermal Hall conductivity, thus
violating the Wiedemann-Franz law.
