Miss Thomas tells Bud that she wants him to stay in chapter 16. Bud's immediate reaction is a "gigantic smile" which he says "split [his] face in half." This implies that he is very happy. The metaphor, in which the smile is described as splitting his face "in half," emphasizes how broadly he is smiling and thus how extremely happy he is.
Explanation:
Miss Thomas tells Bud that they want Bud to stay with them for an indefinite amount of time, which is music to Bud’s ears. All he’s ever wanted was for a family to want him, and now he has just that, even though the band family is nontraditional. He also seems to be comfortable with having the family be the other band members rather than Herman, suggesting that he’s no longer pinning all his hopes on having a relationship with his “father.”
