It has been shown through the use of computer-based models that it is possible purposefully to control the molecular weight and molecular weight distribution of the products from living polymerisation processes by using appropriate forcing functions for the reagent feeds to different types of flow reactors. The algorithm which has been developed is unique in that explicit molecular weight distribution (MWD) envelopes are generated very rapidly. The work described here relates specifically to an ideal single-stage continuous-flow stirred tank reactor (CSTR); i.e. it has been assumed that the living polymerisation chemistry is devoid of mechanistic complexity, that isothermal conditions are maintained throughout reaction, and that the reactors behave in an ideal manner. However, the predictive capacity of the models is not constrained by these assumptions and can be extended to accommodate any type of living polymerisation process and more complex reactor conditions. The predictions of the theoretical model obtained by computer simulation show good agreement with experiment and the algorithm itself has been tested using a number of mathematical and computational procedures; details of this work are presented in Part 2.