  This paper is an enhancement of the previous note "Explicit computations of
Zariski decompositions on P_Z^1". In this paper, we observe several properties
of a certain kind of an arithmetic divisor D on the n-dimensional projective
space over Z and give the exact form of the Zariski decomposition of D on the
projective line over Z. Further, we show that, if n>=2 and D is big and
non-nef, then, for any birational morphism f: X --> P^n_Z of projective,
generically smooth and normal arithmetic varieties, we can not expect a
suitable Zariski decomposition of f^*(D). We also give a concrete construction
of Fujita's approximation of D.
