4 problems

Branch-type conjecture. For sufficiently large $n$, minimal-ABC trees have only $B_3$-branches besides the big vertices.

Star conjecture. The subgraph of a minimal-ABC tree induced by its big vertices is a star.

Structural conjecture. For sufficiently large orders, a minimal-ABC tree is comprised solely of a root vertex and $D_z$- and $D_{z+1}$-branches.

The $B_3$-branch structural conjecture. $B_3$-branches are the main structural component of ABC-minimal trees.