  The end state of a coalescing binary of compact objects depends strongly on
the final total mass M and angular momentum J. Since gravitational radiation
emission causes a slow evolution of the binary system through quasi-circular
orbits down to the innermost stable one, in this paper we examine the
corresponding behavior of the ratio J/M^2 which must be less than 1(G/c) or
about 0.7(G/c) for the formation of a black hole or a neutron star
respectively. The results show cases for which, at the end of the inspiral
phase, the conditions for black hole or neutron star formation are not
satisfied. The inclusion of spin effects leads us to a study of precession
equations valid also for the calculation of gravitational waveforms.
