  We introduce a simple model to self-consistently connect the growth of
galaxies to the formation history of their host dark matter haloes. Our model
is defined by two simple functions: the "baryonic growth function" which
controls the rate at which new baryonic material is made available for star
formation, and the "physics function" which controls the efficiency with which
this material is converted into stars. Using simple, phenomenologically
motivated forms for both functions that depend only on a single halo property,
we demonstrate the model's ability to reproduce the z=0 red and blue stellar
mass functions. Furthermore, by adding redshift as a second input variable to
the physics function we show that the reproduction of the global stellar mass
function out to z=3 is improved. We conclude by discussing the general utility
of our new model, highlighting its usefulness for creating mock galaxy samples
which have a number of key advantages over those generated by other techniques.
