  We revisit the gradient descent dynamics of the spherical
Sherrington-Kirkpatrick ($p=2$) model with finite number of degrees of freedom.
For fully random initial conditions we confirm that the relaxation takes place
in three time regimes: a first algebraic one controlled by the decay of the
eigenvalue distribution of the random exchange interaction matrix at its edge
in the infinite size limit; a faster algebraic one determined by the
distribution of the gap between the two extreme eigenvalues; and a final
exponential one determined by the minimal gap sampled in the disorder average.
We also analyse the finite size effects on the relaxation from initial states
which are almost projected on the saddles of the potential energy landscape,
and we show that for deviations scaling as $N^{-\nu}$ from perfect alignment
the system escapes the initial configuration in a time-scale scaling as $\ln N$
after which the dynamics no longer "self-averages" with respect to the initial
conditions. We prove these statements with a combination of analytic and
numerical methods.
