Final answer:
The structure in question with membranous stacks is the Golgi apparatus, an organelle that packages and ships proteins within and outside of the cell.
Step-by-step explanation:
The structure described as non-uniform with membranous stacks called cisternae, flattened, pancake-like stacks of membranous vesicles, tubular connections between the stacks, and location near the nucleus and centrosome, refers to the Golgi apparatus. The Golgi apparatus functions similarly to a post office within the cell, modifying, sorting, packaging, and shipping proteins and lipids to their appropriate destinations. Vesicles that contain proteins from the rough endoplasmic reticulum fuse with the cis face of the Golgi apparatus where they are modified, and then vesicles pinch off from the trans face to carry the proteins to various locations, including for export out of the cell. Plant and animal cells contain this organelle, though plant cells may have several hundred Golgi stacks scattered throughout the cytoplasm. It is an integral part of the cell's endomembrane system, which also includes the endoplasmic reticulum and vesicles.