  Entanglement sharing among sites of one-particle states is considered using
the measure of concurrence. These are the simplest in an hierarchy of
number-specific states of many qubits and corresponds to ``one-magnon'' states
of spins. We study the effects of onsite potentials that are both integrable
and nonintegrable. In the integrable case we point to a metal-insulator
transition that reflects on the way entanglement is shared. In the
nonintegrable case the average entanglement content increases and saturates
along with a transition to classical chaos. Such quantum chaotic states are
shown to have universal concurrence distributions that are modified Bessel
functions derivable within random matrix theory. Time-reversal breaking and
time evolving states are shown to possess significantly higher entanglement
sharing capacity that eigenstates of time-reversal symmetric systems. We use
the ordinary Harper and kicked Harper Hamiltonians as model systems.
