More than likely not. But, it's important to look at why BPD is occurring in the first place. Some parts of BPD could be due to genetics. This could potentially put children at greater risk for developing BPD. BPD also has a lot to do with environmental factors. The great news is you, as the parent, are in a great deal of control over this. So even though we have no control over our genetics, we do know that we can control the environmental factors a majority of the time, and therefore we have a very strong influence on whether or not people that have the genes to develop BPD will actually end up developing it.
There is always a possibility of genetics affecting children when it comes to accurately diagnoses mental disorders; however, there is not concrete evidence that if you are BPD you are likely to have BPD children. It may or may not happen, but concerning yourself about that risk may rob you of the greatest gift one can enjoy, which is the beauty of children.
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Related Questions: I am thinking of having a baby real soon, but I have BPD. Can my baby get this as well?