  It was shown long back in \cite{Dadhich97} that a non-extremal black hole
cannot be converted into an extremal one by test particle adiabatic accretion.
The Buchdahl star is the most compact object without horizon and is defined by
$\Phi(R) = 4/9$, while black hole by $\Phi(R) = 1/2$. Here $\Phi(R)$ is the
gravitational potential experienced by a particle, radially falling for static
and axially for the rotating object. In this short note we examine the question
of extremalization of the Buchdhal star and show that the same result holds
good as for the black hole. That is, a non-extremal Buchdahl star cannot be
extremalized by test particle accretion. Further since extremal limit for BS is
$>1$, it could facilitate formation of extremal black holes by neutral and
spinless accretion. That is perhaps the only way they could be formed.
