  We study optimal approximation of stochastic processes by polynomial splines
with free knots. The number of free knots is either a priori fixed or may
depend on the particular trajectory. For the $s$-fold integrated Wiener process
as well as for scalar diffusion processes we determine the asymptotic behavior
of the average $L_p$-distance to the splines spaces, as the (expected) number
$k$ of free knots tends to infinity.
