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The space of quantum Hamiltonians has a natural partition in classes ofoperators that can be adiabatically deformed into each other. We considerparametric families of Hamiltonians acting on a bi-partite quantum state-space.When the different Hamiltonians in the family fall in the same adiabatic classone can manipulate entanglement by moving through energy eigenstatescorresponding to different value of the control parameters. We introduce anassociated notion of adiabatic entangling power. This novel measure is analyzedfor general $d\times d$ quantum systems and specific two-qubits examples arestudiedComment: 5 pages, LaTeX, 2 eps figures included. Several non minor changes  made (thanks referee) Version to appear in the PR

Quantum entangling power of adiabatically connected Hamiltonians