We study rooted spiral trees in 2,3 and 4 dimensions on a hyper cubicallattice using exact enumeration and Monte-Carlo techniques. On the squarelattice, we also obtain exact lower bound of 1.93565 on the growth constant$\lambda$. Series expansions give $\theta=-1.3667\pm 0.001$ and $\nu =1.3148\pm0.001$ on a square lattice. With Monte-Carlo simulations we get theestimates as $\theta=-1.364\pm0.01$, and $\nu = 1.312\pm0.01$. These resultsare numerical evidence against earlier proposed dimensional reduction by fourin this problem. In dimensions higher than two, the spiral constraint can beimplemented in two ways. In either case, our series expansion results do notsupport the proposed dimensional reduction.
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