We explore different aspects of the multi-stage fracturing process such as stress interaction between growing hydraulic fractures, perforation friction, as well as the wellbore flow dynamics using a specifically developed numerical solver. In particular, great care is taken to appropriately solve for the fluid partition between the different growing fractures at any given time. We restrict the hydraulic fractures to be fully contained in the reservoir (fractures of constant height) thus reducing the problem to two dimensions. After discussions of the numerical algorithm, a number of verification tests are presented. We then define via scaling arguments the key dimensionless parameters controlling the growth of multiple hydraulic fractures during a single pumping stage. We perform a series of numerical simulations spanning the practical range of parameters to quantify which conditions promote uniform versus non-uniform growth. Our results notably show that, although large perforations friction helps to equalize the fluid partitioning between fractures, the pressure drop in the well along the length of the stage has a pronounced adverse effect on fluid partitioning as a result on the uniformity of growth of the different hydraulic fractures.