The Mill has two forms of Branch-like operations: those with carried belt arguments and those without. Either can have additional belt arguments for a predicate and/or label pointer. Branches without carried arguments do not modify the belt; the target sees the same belt that the branch did. Branches with carried arguments replace the belt contents with the argument list, essentially the same way a call does.
In your example, the branch from EBB-A to EBB-B is likely to not have carried arguments; EBB-B will start with EBB-A’s belt as of the branch. In contrast, both branches to EBB-C will have carried arguments conveying the values needed by EBB-C. The inbound carried argument lists will have the same number of entries (possibly zero, up to the belt size) and the entries will have matching widths, so EBB-C will start with a congruent belt regardless of which path was taken.
In addition, when a branch is taken there may be a functional unit at work on a long-latency operation that has not yet retired. This is not a problem for branches without carried args; EBB-A can start an operation that will retire in EBB-B, because the belt in EBB-B is unambiguous both before and after the retire. In principle, the same could be done over branches that have carried args, but only if every source of an inbound branch arranged to have its long-latency operation retire at the same point in the target. Such a coincidence is extremely far-fetched and the specializer does not attempt to use it. Instead, it forces all operations (except loads) to have retired before any branch with carried args.
Loads are the exception, and the Mill has the special Pickup Load form to deal with loads that retire across arg-carrying branches. A pickup load operation carries a tag and does not retire normally. Instead, sometime later the code can issue a Pickup operation with the same tag and get the retire dropped to the belt. The Load and its Pickup can be in different ebbs; the only requirement is that each Load must eventually be picked up, and each pickup must have a previous load with the same tag.