Hyperband distributions of affine spaces

We consider a special class of hyperband distributions, $\mathfrak{H}(L)$-distributions, with the incidence relation $A\in L(A)\subset H(A)$. The theory of $\mathfrak{H}(L)$-distributions is used for studying torso surfaces, regular one-dimensional hyperbands, special classes of hyperbands, and hypersurfaces of an affine space.