The almost-all-trees conjecture for local antimagic chromatic number

Let $T$ be a tree with $k$ pendant vertices. The families $K(2;a,b)$ and $Ct(3;a,0,b)$ are the exceptional tree families described in the supplied statement. Almost-all-trees conjecture. Almost all trees with $k$ pendant vertices have $\chi_{la}=k+1$; alternatively, all such trees have $\chi_{la}=k+1$ except $K(2;a,b)$ with $b\ge a\ge2$ and $a<b(b+1)/2$, and $Ct(3;a,0,b)$ with $a\le b<(a+2)(a-1)/3$ and $a+b\equiv0,3\pmod{4}$. This is an informal and explicitly hedged formulation, with the proposed precise alternative left unresolved; it should be checked against the later formal tree conjecture.