  We study the spectrum $M_b(U)$ of the algebra of bounded type holomorphic
functions on a complete Reinhardt domain in a symmetrically regular Banach
space $E$ as an analytic manifold over the bidual of the space. In the case
that $U$ is the unit ball of $\ell_p$, $1<p<\infty$, we prove that each
connected component of $M_b(B_{\ell_p})$ naturally identifies with a ball of a
certain radius. We also provide estimates for this radius and in many natural
cases we have the precise value. As a consequence, we obtain that for connected
components different from that of evaluations, these radii are strictly smaller
than one, and can be arbitrarily small. We also show that for other Banach
sequence spaces, connected components do not necessarily identify with balls.
