This paper characterizes the development of modular branching structures that satisfy three assumptions: (a) subapical branching, meaning that new branches can be created only near the apices of the existing branches, (b) finite number of module types and states, and (c) absence of interactions between coexisting components of the growing structure. These assumptions are captured in the notion of subapical bracketed deterministic L-systems without interactions (sBDOL-systems). We present the biological rationale for sBDOL-systems and prove that it is decidable whether a given BDOL-system is subapical or not. In addition, using the assumption that modules, once created, continue to exist, we show that (propagating) sBDOL-sytems are too weak to generate acrotonic and mesotonic branching structures which are often observed in nature. Their development must therefore be controlled by more involved mechanisms, overriding at least one of the assumptions (a-c) above.