(Abridged) We study the outer density profiles of dark matter haloes predicted by a generalized secondary infall model and observed in a N-body cosmological simulation of a Lambda CDM model. We find substantial systematic variations in shapes and concentrations of the halo profiles as well as a strong correlation of the profiles with the environment. In the N-body simulation, the average outer slope of the density profiles, beta (rhopropto r^{-beta}), of isolated haloes is approx 2.9; 68% of these haloes have values of beta between 2.5 and 3.8. Haloes in dense environments of clusters are more concentrated and exhibit a broad distribution of beta with values larger than for isolated haloes . Contrary to what one may expect, the haloes contained within groups and galaxy systems are less concentrated and have flatter outer density profiles than the isolated haloes. The concentration decreases with M_h, but its scatter for a given mass is substantial. The mass and circular velocity of the haloes are strongly correlated: M_h propto V_m^{alpha} with alpha ~ 3.3 (isolated) and ~3.5 (haloes in clusters). For M_h=10^12M_sun the rms deviations from these relations are Delta logM_h=0.12 and 0.18, respectively. Approximately 30% of the haloes are contained within larger haloes or have massive companions (larger than ~0.3 the mass of the current halo) within 3 virial radii. The remaining 70% of the haloes are isolated objects. The distribution of beta as well as the concentration-mass and M_h-V_m relations for the isolated haloes agree very well with the predictions of our seminumerical approach which is based on a generalization of the secondary infall model and on the extended Press-Schechter formalism.
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