There was a British study done in the 1990s that showed the rate of abuse against children was over 30 times higher in homes where a single-mother was living with a boyfriend who was not the child’s father, than in homes where children lived with both birth parents.
Also, in the statistic quoted in this article, I believe research has also shown that single mothers are less likely to report violence against their child if the “perp” is their live-in boyfriend.
It’s always the “boyfriend” an irresponsible crum bum that is in it for the short term sex