  In this article, several 2+1 dimensional lattice hierarchies proposed by
Blaszak and Szum [J. Math. Phys. {\bf 42}, 225(2001)] are further investigated.
We first describe their discrete zero curvature representations. Then, by means
of solving the corresponding discrete spectral equation, we demonstrate the
existence of infinitely many conservation laws for them and obtain the
corresponding conserved densities and associated fluxes formulaically. Thus,
their integrability is further confirmed.
