Via TRAC:

"Despite the concern about the number of families arriving at the border seeking asylum, families continue to remain a minor proportion of new cases arriving at the Immigration Courts each month. For example, during March 2019, just 18.7 percent of the new cases that came in involved these families. Despite this, the court's backlog continues to climb and reached a new historic high of 869,013 cases on its active docket at the end of March.

After being released in border communities, families seldom remain there. Since September 2018, 32 courts in 24 states have received at least 100 new family cases. Over half of these cases are before courts headquartered in sanctuary cities. Among the top ten courts where family cases are located, six are usually classified as sanctuary jurisdictions. These courts include those in New York City, San Francisco, Los Angeles and Chicago."