Models of stationary, axisymmetric, non-self-gravitating tori around s
tellar mass Kerr black holes are calculated. Such objects may form as
a result of a merger between two neutron stars, a neutron star and a s
tellar mass black hole, or a ''failed supernova'' collapse of a single
rapidly rotating star. We explore a large range of parameters: the bl
ack hole mass and angular momentum, the torus mass, angular momentum a
nd entropy. Physical conditions within the tori are similar to those i
n young and hot neutron stars, but their topology is different, and th
e range of masses and energies is much larger. A possible relevance of
our models and gamma-ray bursts is discussed.