  We study affine fusion with the adjoint representation. For simple Lie
algebras, elementary and universal formulas determine the decomposition of a
tensor product of an integrable highest-weight representation with the adjoint
representation. Using the (refined) affine depth rule, we prove that equally
striking results apply to adjoint affine fusion. For diagonal fusion, a
coefficient equals the number of nonzero Dynkin labels of the relevant affine
highest weight, minus 1. A nice lattice-polytope interpretation follows, and
allows the straightforward calculation of the genus-1 1-point adjoint Verlinde
dimension, the adjoint affine fusion tadpole. Explicit formulas, (piecewise)
polynomial in the level, are written for the adjoint tadpoles of all classical
Lie algebras. We show that off-diagonal adjoint affine fusion is obtained from
the corresponding tensor product by simply dropping non-dominant
representations.
