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Let G be a connected reductive algebraic group defined over an algebraically closed field 
of characteristic 0. We consider the commuting variety 
of the nilradical 
of the Lie algebra 
of a Borel subgroup B of G. In case B acts on with only a finite number of orbits, we verify that is equidimensional and that the irreducible components are in correspondence with the distinguishedB-orbits in . We observe that in general is not equidimensional, and determine the irreducible components of in the minimal cases where there are infinitely many B-orbits in .
