No. If you have BPD, your kids are at greater risk of having BPD themselves. But, there is also a good chance that they will not have BPD. And, there are things you can do to reduce their risk.
There is research showing that BPD runs in families. This is likely due to a number of factors. First, some part of BPD is due to genetics; if these are your biological kids and they have inherited a certain combination of genes from you, they may be more at risk to develop BPD.
Second, the types of environments that can put children at risk of developing BPD also run in families. For example, someone who is maltreated as a child is at greater risk to develop BPD. That person is also at greater risk of having difficulty parenting. It is hard to be an effective parent when you are struggling with BPD symptoms, and it does not help if you did not have good parenting models yourself.
However, none of this means that your children will have BPD. While there is nothing you can do about genetics, if your kids live with you, there is a great deal you can do about environmental factors. And, there is evidence that environment has a very strong influence on whether or not people with the genes for BPD actually develop the disorder.
The first thing that you can do is to get treatment for yourself. People who undergo an effective treatment for BPD under the guidance of a mental health professional can improve significantly. Some people no longer meet diagnostic criteria for BPD after they finish treatment. Having less symptoms means having more resources for effective parenting.
Once you are in treatment, you can also express your concerns about your children to your care provider, and ask them for help. Your provider can help you to evaluate your home environment and whether your symptoms could be affecting your parenting skills. They may even be able to refer you to programs that help people build skills to be more effective parents. People with BPD can be very effective and nurturing parents, but because the symptoms of BPD can be very intense, for many it does take some work.
Lis E, Greenfield B, Henry M, Guile JM, Dougherty G. "Neuroimaging and Genetics in Borderline Personality Disorder: A Review." Journal of Psychiatry and Neuroscience, 32:162-173, 2007.
Zanarini MC, and Frenkenburg FR. "Pathways to the Development of Borderline Personality Disorder." Journal of Personality Disorders, 11:93-104, 1997.