  In our previous paper [math.NT/0408050], we established a correspondence
between vector-valued holomorphic Siegel modular forms and cohomology with
local coefficients for local symmetric spaces $X$ attached to real orthogonal
groups of type $(p,q)$. This correspondence is realized using theta functions
associated to explicitly constructed "special" Schwartz forms. Furthermore, the
theta functions give rise to generating series of certain "special cycles" in
$X$ with coefficients.
  In this paper, we study the boundary behaviour of these theta functions in
the non-compact case and show that the theta functions extend to the Borel-Sere
compactification $\bar{X}$ of $X$. However, for the $\Q$-split case for
signature $(p,p)$, we have to construct and consider a slightly larger
compactification, the "big" Borel-Serre compactification. The restriction to
each face of $\bar{X}$ is again a theta series as in [math.NT/0408050], now for
a smaller orthogonal group and a larger coefficient system.
  As application we establish the cohomological nonvanishing of the special
(co)cycles when passing to an appropriate finite cover of $X$. In particular,
the (co)homology groups in question do not vanish.
