Star Battle technique: region group
When two or three rows or columns can only hold stars from the same number of regions, those regions are used up and their other cells can be crossed out.
This is the counting technique. If k rows (or columns) together contain stars for exactly k regions, because the cells of those rows are covered only by those k regions, then those regions' stars must lie inside those rows. Every cell of those regions that lies outside the rows is out. The reverse also holds.
Example with two lines
Example from a real Pencilmark puzzle (#79, 7×7). Solver explanation: “Cols 2, 3 can only hold stars from regions 4, 6. Those regions are used up there, so cross out their cells in other cols.”
Example with three lines
Example from a real Pencilmark puzzle (#104, 8×8). Solver explanation: “Cols 1, 2, 3 can only hold stars from regions 1, 6, 7. Those regions are used up there, so cross out their cells in other cols.”
How to spot it
Count: for a set of lines, how many different regions still have candidate cells in them? If that number equals the number of lines, you have a group. Start with pairs of adjacent lines, then triples.
Most hard puzzles need at least one group. Pencilmark's expert puzzles may need groups of three.