The mechanism for nucleus centering in mouse oocytes results from a gradient of actin-positive vesicles. By microinjecting oil droplets and fluorescent beads, we analyze the consequences of the gradient of activity on transport of exogenous tracer particles of different sizes. We also use optical tweezers to probe rheological properties of the cytoplasm. We find that the gradient activity induces a general centering force, akin to an effective pressure gradient, leading to centering of oil droplets with velocities comparable to nuclear ones. High temporal resolution measurements reveal that passive particles, larger than 1”m, experience the activity gradient by a biased diffusion towards the cell center. Unexpectedly, this general and size dependent mechanism is maintained in Meiosis I but contrasted by a further process that specifically off-centers the spindle. These antagonizing processes depend on myosin activity, thus we reconcile how the same molecular actors can have two opposite functions (centering versus off-centering).