  Let $P$ be a prime polynomial in the variable $Y$ over a finite field and let
$f$ be a quadratic irrational in the field of formal Laurant series in the
variable $Y^{-1}$. We study the asymptotic properties of the degrees of the
coefficients of the continued fraction expansion of quadratic irrationals such
as $P^nf$ and prove results that are in sharp contrast to the analogue
situation in zero characteristic.
