  In this paper we derive analytical relations between probabilities of the
excited state transfers and entanglements calculated by both the Wootters and
positive partial transpose (PPT) criteria for the arbitrary spin system with
single excited spin in the external magnetic field and Hamiltonian commuting
with $I_z$. We apply these relations to study the arbitrary state transfers and
entanglements in the simple systems of nuclear spins having two- and
three-dimensional geometrical configurations with $XXZ$ Hamiltonian. It is
shown that High-Probability State Transfers (HPSTs) are possible among all four
nodes placed in the corners of the rectangle with the proper ratio of sides as
well as among all eight nodes placed in the corners of the parallelepiped with
the proper ratio of sides. Entanglements responsible for these HPSTs have been
identified.
