  This report studies local asymptotics of P-splines with $p$th degree
B-splines and a $m$th order difference penalty. Earlier work with $p$ and $m$
restricted is extended to the general case. Asymptotically, penalized splines
are kernel estimators with equivalent kernels depending on $m$, but not on $p$.
A central limit theorem provides simple expressions for the asymptotic mean and
variance. Provided it is fast enough, the divergence rate of the number of
knots does not affect the asymptotic distribution. The optimal convergence rate
of the penalty parameter is given.
