“I pay them all when I have the money, but some months are tougher than others,” said Mr. Pantoja, whose outdoor nightclub, Caribe, lures patrons on weekend nights who cling to one another under its strobe lights.

One of the court’s clerks interjected, telling Mr. Pantoja, “Frankly, you just have to stop making more children.” Then the judge issued a quick verdict, ordering the defendant to honor his financial obligations to his ex-wife or be jailed for three months.

As Ms. de Paula smiled at the outcome, Mr. Pantoja scowled.

“The authorities on this boat don’t rely on facts, but on gossip,” he said. “At least I’ll have children to carry my coffin when I die.”

Throughout the day, others shuffled onto the boat. Some sought the other services available onboard, receiving social security cards, voting papers and water purification tablets.