Triple graph grammars (TGGs) are a common formalism to specify model transformations in a relational way, creating source and target models together with their correspondences. The classical theoretical model of triple graphs is based on a morphism span from the correspondence component to the source and target components. In practice, this formalization often can not be used as for certain applications no proper morphisms between the correspondence and source or target components can be found. In this paper, we introduce TGGs as plain graph grammars with special typing which avoids an extra flattening step and is more directly suitable for implementation and formal analysis due to the more flexible and homogeneous formalization. The typing expresses that each graph can be partitioned into a source, correspondence, and target component allowing arbitrary relationships between the components. We further show that the main decomposition and composition result, which is the formal basis for correctness, completeness, consistency, and functional behavior, holds analogous to the classical approach and demonstrate that classical triple graph transformation is actually a special case – after flattening – of the more flexible one.