In November, 2013, New Jersey became the third US state to permit gambling over the internet, following Nevada and Delaware, and the state expanded its self-exclusion program with options involving internet gambling. People on New Jersey's casino self-exclusion list automatically had their exclusion extended to internet gambling. This is in keeping with the fact that New Jersey's exclusion program does not currently allow, it seems, someone to exclude from casinos while maintaining the option to bet on the internet. The opposite configuration, where a person can exclude from the internet but not from the bricks-and-mortar casinos, is available in New Jersey, however.
New Jersey appears poised to alter its self-exclusion rules, which currently require self-excluders to confess to being a "problem gambler." There can be many motives to self-exclude, and not everyone who wants to self-exclude is a problem gambler. [I haven't checked, but my suspicion is that many jurisdictions have a similar admission required for their self-exclusion agreements. While I am engaging in uninformed speculation, I think that this language might have been thought important to provide legal protection for casinos attempting to enforce exclusion agreements. And if I can continue speculating wildly, the change in New Jersey law may have been sparked by some old fashioned journalism.]
Currently, only adults located within the state borders can engage in internet gambling. (This is true for all three of the states that currently offer legal internet gambling.) Some lawmakers in New Jersey are looking to alter that situation.