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Mary Cosby 's son Robert Jr. has found himself in hot water with the law again ... we've learned he's been arrested for a number of alleged crimes, including assault and trespassing.

According to an arrest report, obtained by TMZ ... "The Real Housewives of Salt Lake City" star's only child was arrested just outside Salt Lake City, UT Saturday for failure to stop at the command of law enforcement, criminal trespassing, assault, and 3 alleged violations of a court order.

Per the report, local police responded to a domestic violence call after Robert Jr. allegedly tried to break into his father-in-law's home via a dog door and assaulted someone on the front lawn.

Robert Jr. allegedly failed to get on the ground when ordered to do so by the responding police officer ...

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