We analyze the topological Hall conductivity (THC) of topologically nontrivial spin textures like magnetic
vortices and skyrmions and investigate its possible application in the readback for magnetic memory based
on those spin textures. Under adiabatic conditions, such spin textures would theoretically yield quantized
THC values, which are related to topological invariants such as the winding number and polarity, and as
such are insensitive to fluctuations and smooth deformations. However, in a practical setting, the finite size
of spin texture elements and the influence of edges may cause them to deviate from their ideal
configurations. We calculate the degree of robustness of the THC output in practical magnetic memories in
the presence of edge and finite size effects.