  We study pairs $(\Gamma,G)$, where $\Gamma$ is a 'Buekenhout-Tits'
pregeometry with all rank 2 truncations connected, and $G\leqslant\mathrm{Aut}
\Gamma$ is transitive on the set of elements of each type. The family of such
pairs is closed under forming quotients with respect to $G$-invariant
type-refining partitions of the element set of $\Gamma$. We identify the
'basic' pairs (those that admit no non-degenerate quotients), and show, by
studying quotients and direct decompositions, that the study of basic
pregeometries reduces to examining those where the group $G$ is faithful and
primitive on the set of elements of each type. We also study the special case
of normal quotients, where we take quotients with respect to the orbits of a
normal subgroup of $G$. There is a similar reduction for normal-basic
pregeometries to those where $G$ is faithful and quasiprimitive on the set of
elements of each type.
