  We introduce the notion of semibreak divisors on metric graphs (tropical
curves) and prove that every effective divisor class (of degree at most the
genus) has a semibreak divisor representative. This appropriately generalizes
the notion of break divisors (in degree equal to genus). Our method of proof is
new, even for the special case of break divisors. We provide an algorithm to
efficiently compute such semibreak representatives. Semibreak divisors provide
the tool to establish some basic properties of effective loci inside Picard
groups of metric graphs. We prove that effective loci are pure-dimensional
polyhedral sets. We also prove that a `generic' divisor class (in degree at
most the genus) has rank zero, and that the Abel-Jacobi map is `birational'
onto its image. These are analogues of classical results for Riemann surfaces.
