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We used high resolution dark matter only cosmological simulations toinvestigate the structural properties of Lambda Cold Dark Matter ($\Lambda$CDM)haloes over cosmic time. The haloes in our study range in mass from $\sim10^{10}$ to $\sim 10^{12} \mathrm{M}_\odot$, and are resolved with $10^5$ to$10^7$ particles. We fit the spherically averaged density profiles of DM haloeswith the three parameter Einasto function. For our sample of haloes, theEinasto shape parameter, $\alpha$, is uncorrelated with the concentration, $c$,at fixed halo mass, and at all redshifts. Previous reports of ananti-correlation are traced to fitting degeneracies, which our fits are lesssensitive to due to our higher spatial resolution. However, for individualhaloes the evolution in $\alpha$ and $c$ is anti-correlated: at redshift $z=7$,$\alpha \simeq 0.4$ and decreases with time, while $c\simeq 3$ and increaseswith time. The evolution in structure is primarily due to accretion of mass atlarger radii. We suggest that $\alpha$ traces the evolutionary state of thehalo, with dynamically young haloes having high $\alpha$ (closer to a top-hat:$\alpha^{-1}=0$), and dynamically relaxed haloes having low $\alpha$ (closer toisothermal: $\alpha=0$). Such an evolutionary dependence reconciles theincrease of $\alpha$ vs peak height, $\nu$, with the dependence on the slope ofthe power spectrum of initial density fluctuations found by previous studies.

A deeper look into the structure of {\Lambda}CDM haloes: correlations between halo parameters from Einasto fits