  We generalize the concept of $r$-point clusters of a scheme $S$ to
$r$-relative clusters of a $B$-scheme $\mathcal{S}$. Define schemes $Cl_r$ that
naturally parametrize the $r$-relative clusters which generalize the Kleiman's
construction of the iterated blowups by $r$-point clusters. We show that the
iterated construction of $Cl_{r+1}$ from $Cl_{r}$ is something more than just
to do a blow up of $Cl_r\times_{Cl_{r-1}} Cl_r$ at the diagonal. We show a few
simple examples illustrating the situations that may occur.

Algebraic Geometry