  The space of quantum Hamiltonians has a natural partition in classes of
operators that can be adiabatically deformed into each other. We consider
parametric families of Hamiltonians acting on a bi-partite quantum state-space.
When the different Hamiltonians in the family fall in the same adiabatic class
one can manipulate entanglement by moving through energy eigenstates
corresponding to different value of the control parameters. We introduce an
associated notion of adiabatic entangling power. This novel measure is analyzed
for general $d\times d$ quantum systems and specific two-qubits examples are
studied
