Some interesting behaviour of accreting particles in the gap region between the horizon of the Kerr black hole and the inner edge of the surrounding disc is investigated. The following results are obtained. (i) Spacetime coincidence of the maximum of angular velocity of accreting particles and that of the black hole horizon is extended to the more general disc-accretion. (ii) The possibility is discussed of negative energy of accreting particles in prograde orbit inside the ergosphere of the Kerr black hole, which is surrounded by strong enough magnetic field.