glossary
Common-centroid
Common-centroid placement puts two groups of unit devices on the same center of mass, so a smooth gradient hits both the same way.

The fingers alternate around one shared center. The small blocks at the ends are not part of the pair.
A wafer is not uniform. Thickness, temperature, and stress tilt across a block. If device A lives on the left and device B on the right, they disagree. Interleave them as ABBA around one center and a linear tilt cancels. A differential pair made of four 2 micrometer units in an ABBA box is a textbook picture: a 2 by 2 or 4 by 4 quilt of identical transistors with crossed connections. The net wiring looks busier. The match is the point. Common-centroid is one tool of matching. It does not fix a device rotated the wrong way, or a via farm that heats only one side. Keep unit cells identical, including dummies at the edges.
Any interleaving is not automatically common-centroid. A stripe ABABAB shares a center only if the counts and the ends are honest. Sketch the centroids if the centers are in doubt. Wiring can ruin a pretty quilt. If all A drains snake out the left and all B drains out the right, the gradient returns in metal. A common-centroid pair has symmetric via counts and a shared dummy ring. Sketch the two centroids on paper. If they do not land on the same point, the name is marketing.
How devices are matched in the drawing and how analog blocks are arranged are covered in analog layout: matching, dummies, and guard rings; how the unit cells are stamped is in cells and instances.