  In a previous work arXiv:0903.4512, we have built an homotopical Turaev-Viro
invariant and an HQFT from the universal graduation of a spherical category. In
the present paper, we show that every graduation $(G,p)$ of a spherical
category $\C$ defines an homotopical Turaev-Viro invariant $HTV_{\C}^{(G,p)}$
and an HQFT $\m{H}_{\C}^{(G,p)}$. Furthermore we show that the Turaev-Viro TQFT
will be split into blocks coming the HQFT $\m{H}_{\C}^{(G,p)}$. We show that
this decomposition is maximal for the universal graduation of the category,
which means that for every graduation $(G,p)$ the HQFT $\m{H}_{\C}^{(G,p)}$ is
split into blocks coming from the HQFT obtained from the universal graduation.
