If a tree doesn't contain the full set of species (i.e. if the tree is partial), all branches of that tree differ from branches of full trees.
To allow merging such trees with other trees, the set of missing species is added once to each side of each branch, adding two hypothetical branches to the branch pool (hypothetical in that way, that they do not necessarily occur in any tree).
These two hypothetical branches are added with different probabilities:
adding missing species to the bigger side of a branch is done with a probability of 1.0
adding missing species to the smaller side of a branch is done with a probability P calculated as follows:
S = number of edges on the SMALL side of the branch + 1
B = number of edges on the BIG side of the branch + 1
M = number of missing species
That probability tends towards zero for leaf branches and towards 1.0 for center branches.
If you merge nearly identical topologies, which only differ by some species removed from some of the topologies, the resulting bootstrap values reflect the number of trees the species occurred in (e.g. 67% if species occurred in 2 of 3 trees).
Another kind of branches is completely artificial: a branch with the missing species on one side and all species from the partial tree on the other side. These artificial branches will ONLY be considered for the output topology, if no other tree defines such a branch and if it's absolutely necessary to build a connected topology.
Since nothing is known about the length of such an artificial branch, a distance of 1.0 will be assumed (e.g. happens when you merge disjunct trees) and a zero bootstrap value will be written to the output tree.