The churches of Asia send greetings. Aquila and Prisca, together with the church in their house (), greet you warmly in the Lord. (1 Cor 16:19)
Greet Prisca and Aquila .... Greet also the church in their house. (Rom 16:3-5)See also Col 4:15 and Philemon 2.
Now, it was common for whole households to follow the faith of the head of the house (Acts 10:2: 16:15; 16:29-34; 18:8; 1 Cor 16:15). In light of this, E.A. Judge has suggested that the phrase "the church in their house" may simply refer to the assembly of believers who were members of that particular household (Social Distinctives of the Christians in the First Century p25). The assembly in the house of Aquila and Prisca may have comprised only their family members and servants. I offer the following observations which support this view.
1. Aquila and Prisca and, presumably, the members of their household had previously been part of the Corinthian church, so they would naturally want to send greetings to Corinth after moving to Ephesus (1 Cor 16:19). It is hard to explain why Paul mentions "the church in their house" as senders of warm greetings if it consisted mainly of Ephesians who had not been part of the Corinthian church. Paul would then have been making an invidious distinction between them and the other Ephesian believers.
2. Similarly, Paul greets the assembly that meets in the house of Prisca and Aquila in Rome (Rom 16:3-5). This is explicable if the members of that assembly were dependents of Prisca and Aquila who had known Paul from their time in Corinth and Ephesus.
3. We have no evidence that Prisca and Aquila formed churches around themselves. In Corinth this role was taken by Titius Justus (Acts 18:7), =Stephanas (1 Cor 16:15), and Crispus (Acts 18:8). In Asia the role was taken by Epaenetus (Rom 16:5) and Paul preached there in the hall of Tyrannus, not from the house of Aquila and Prisca.
4. Prisca and Aquila were with Paul in Ephesus (1 Cor 16:19) shortly before Pentecost (1 Cor 16:8). Paul planned to send the collection to Judea the following spring at the latest (1 Cor 16:3-6). Acts 20:2-6) confirms that the collection was sent in the spring, at the very beginning of the travel season, and there is no reason to suppose that it was a later spring than the one envisaged in 1 Corinthians. Romans was written before this time. Now, if the assembly of believers in the house of Prisca and Aquila in Rom 16:3-5 consisted of people other than the dependents of the couple, then we have a rather compressed chronology. We would have to suppose that Prisca and Aquila travelled to Rome soon after 1 Corinthians was written and that within about 4 months of arrival they established a house church and that someone then traveled from Rome to Corinth before the end of the same travel season and told Paul about this house church. This does not seem likely. Why would believers in Rome so quickly join the house church of Prisca and Aquila in preference to their own house churches? If Prisca and Aquila were successful evangelists, why is there no evidence of this from their time in Corinth or Ephesus? The problems are solved if we suppose that the assembly consisted of dependents of Prisca and Aquila. Paul knew that they had travelled with the couple to Rome and would continue to be part of their household. There is then no need to supposed that Paul had received recent news from Rome.
5. The (putative) author of Colossians had not visited Colossae, yet he appears to have known Nympha and the assembly in her house (Col 4:15). It is possible to imagine Nympha and many believing members of her household visiting Paul (in Ephesus for example). It is hard to imagine that "Paul" would have come to know the members of this assembly if it consisted of members of many households.
For these reasons I think that the assembly of believers in the house of Prisca and Aquila consisted of members of their household.
If this hypothesis is correct we can abandon the romantic notion that Prisca and Aquila travelled to Ephesus and to Rome to plant churches. They were the target of persecution (Rom 16:4) and had left Italy because of persecution (Acts 18:2), so it is most likely that they left Corinth because of persecution, just as Sosthenes did following his beating (Acts 18:17; 1 Cor 1:1). Presumably they returned home to Rome as soon as they could following the death of Claudius.
Some conjecture that Stephanas was the head of a house church cell and that his household placed themselves at the service of the other members of that cell (1 Cor 16:15). This now looks less likely. Rather, as I have argued before, Stephanas was Gaius, the host of the whole church.