We consider the system of $N$ ($\ge2$) elastically colliding hard balls of
masses $m_1,...,m_N$ and radius $r$ in the flat unit torus $\Bbb T^\nu$,
$\nu\ge2$. In the case $\nu=2$ we prove (the full hyperbolicity and) the
ergodicity of such systems for every selection $(m_1,...,m_N;r)$ of the
external geometric parameters, without exceptional values. In higher
dimensions, for hard ball systems in $\Bbb T^\nu$ ($\nu\ge3$), we prove that
every such system (is fully hyperbolic and) has open ergodic components.