alesc

The root alesc comes from Latin alescere, "to grow up," which is the inceptive (beginning-to-happen) form of alere, "to nourish, to feed, to rear." The little -escere ending is important: in Latin it means "to begin to —" or "to gradually become —." So alescere isn't just "to grow"; it's "to start growing, to be in the process of being nourished into something bigger."

The clearest survivor is coalesce: co- (together) + alescere (grow) = "to grow together." Picture two drops of water on a window slowly swelling until they merge into one — that's coalescing. Separate factions coalesce into a single party; scattered ideas coalesce into a plan. The noun coalescence is the merging itself.

From the same "growing together" idea, but through the noun route, comes coalition — a body of groups that have grown together for a shared purpose. A political coalition is several parties merged into one governing bloc. Notice it's the same co- + al- core as coalesce, just frozen into a noun of organization.

The nourishing sense of the parent verb alere shows up in alumnus — literally "one who was nourished," i.e. someone fed and raised by a school. An alumnus is a former student the institution once nurtured. (Its plural, alumni, and the female alumna/alumnae, keep the Latin endings.)

So two threads run through the family: growing together (coalesce, coalescence, coalition) and being nourished into maturity (alumnus). Both come back to one parent picture — feeding something so it grows.