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We show that the Anderson model has a transition from localization todelocalization at exactly 2 dimensional growth rate on antitrees withnormalized edge weights which are certain discrete graphs. The kinetic part hasa one-dimensional structure allowing a description through transfer matriceswhich involve some Schur complement. For such operators we introduce the notionof having one propagating channel and extend theorems from the theory ofone-dimensional Jacobi operators that relate the behavior of transfer matriceswith the spectrum. These theorems are then applied to the considered model. Inessence, in a certain energy region the kinetic part averages the randompotentials along shells and the transfer matrices behave similar as for aone-dimensional operator with random potential of decaying variance. At $d$dimensional growth for $d>2$ this effective decay is strong enough to obtainabsolutely continuous spectrum, whereas for some uniform $d$ dimensional growthwith $d<2$ one has pure point spectrum in this energy region. At exactlyuniform $2$ dimensional growth also some singular continuous spectrum appears,at least at small disorder. As a corollary we also obtain a change fromsingular spectrum ($d\leq 2$) to absolutely continuous spectrum ($d\geq 3)$ forrandom operators of the type $\mathcal{P}_r \Delta_d \mathcal{P}_r+\lambda\mathcal{V}$ on $\mathbb{Z}^d$, where $\mathcal{P}_r$ is an orthogonal radialprojection, $\Delta_d$ the discrete adjacency operator (Laplacian) on$\mathbb{Z}^d$ and $\lambda \mathcal{V}$ a random potential.

Anderson transition at 2 dimensional growth rate on antitrees and spectral theory for operators with one propagating channel