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In continuation of our recent work arXiv:2006.07312, we classify the extremaltraces on infinite diagram algebras that appear in the context of Schur-Weylduality for Banica and Speicher's easy groups. We show that the branchinggraphs of these algebras describe walks on new variations of the Young graphwhich describe curious ways of growing Young diagrams. As a consequence, weprove that the extremal traces on generic rook-Brauer algebras are alwaysextensions of extremal traces on the group algebra $\mathbb{C}[S_{\infty}]$ ofthe infinite symmetric group. Moreover, we conjecture that the same is true forgeneric parameter deformations of the centralizers of the hyperoctahedral groupand we reduce this conjecture to a conceptually much simpler numericalstatement. Lastly, we address the trace classification problem for theSchur-Weyl dual of the halfliberated orthogonal group $O_N^*$, in which caseextremal traces are always extensions of extremal traces on$\mathbb{C}[S_{\infty} \times S_{\infty}]$. Our approach relies on methodsdeveloped by Vershik and Nikitin.

Traces on diagram algebras II: Centralizer algebras of easy groups and new variations of the Young graph