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We present a new algorithm which groups the subhaloes found in cosmologicalN- body simulations by structure finders such as SUBFIND into dark matterhaloes whose formation histories are strictly hierarchical. One advantage ofthese `Dhaloes' over the commonly used friends-of-friends (FoF) haloes is thatthey retain their individual identity in cases when FoF haloes are artificiallymerged by tenuous bridges of particles or by an overlap of their outer diffusehaloes. Dhaloes are thus well-suited for modelling galaxy formation and theirmerger trees form the basis of the Durham semi-analytic galaxy formation model,GALFORM. Applying the Dhalo construction to the LambdaCDM Millennium-2simulation we find that approximately 90% of Dhaloes have a one-to-one,bijective match with a corresponding FoF halo. The remaining 10% are typicallysecondary components of large FoF haloes. Although the mass functions of bothtypes of haloes are similar, the mass of Dhaloes correlates much more tightlywith the virial mass, M200, than FoF haloes. Approximately 80% of FoF andbijective and non-bijective Dhaloes are relaxed according to standard criteria.For these relaxed haloes all three types have similar concentration-M200relations and, at fixed mass, the concentration distributions are describedaccurately by log-normal distributions.

N-body Dark Matter Haloes with simple Hierarchical Histories