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We consider the commuting variety $\\mathcal C(\\mathfrak u)$ of the nilradical $\\mathfrak u$ of the Lie algebra $\\mathfrak b$ of a Borel subgroup $B$ of $G$. In case $B$ acts on $\\mathfrak u$ with only a finite number of orbits, we verify that $\\mathcal C(\\mathfrak u)$ is equidimensional and that the irreducible components are in correspondence with the {\\em distinguished} $B$-orbits in $\\mathfrak u$. 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