  A classical result of Miyanishi-Sugie and Keel-McKernan asserts that for
smooth affine surfaces, affine-uniruledness is equivalent to affine-ruledness,
both properties being in fact equivalent to the negativity of the logarithmic
Kodaira dimension. Here we show in contrast that starting from dimension three,
there exists smooth affine varieties which are affine-uniruled but not
affine-ruled.
