  Motivated by the success of the recently proposed method of anomaly
cancellation to derive Hawking fluxes from black hole horizons of spacetimes in
various dimensions, we have further extended the covariant anomaly cancellation
method shortly simplified by Banerjee and Kulkarni to explore the Hawking
radiation of the (3+1)-dimensional charged rotating black strings and their
higher dimensional extensions in anti-de Sitter spacetimes, whose horizons are
not spherical but can be toroidal, cylindrical or planar, according to their
global identifications. It should be emphasized that our analysis presented
here is very general in the sense that the determinant of the reduced
(1+1)-dimensional effective metric from these black strings need not be equal
to one $(\sqrt{-g} \neq 1)$. Our results indicate that the gauge and energy
momentum fluxes needed to cancel the (1+1)-dimensional covariant gauge and
gravitational anomalies are compatible with the Hawking fluxes. Besides,
thermodynamics of these black strings are studied in the case of a variable
cosmological constant.
