Fighting:
I really depends on the people involved. Between my newly divorced partner and I, we have 5 children...ages range from 25 to 13...and there have been zero issues so far. In fact, its been pretty wonderful for me.
In fact, I'm truly enjoying the blend because my new partner has new grandchildren...which I've had the priviledge of being able to develop a close relationship with. And my children have enjoyed the same experience with him.
Its really a function of taking your time and respecting the previous partner's role as the primary parent. I always listen to my new partner when he needs to vent or confide in me about his longterm marriage. But we do that in private....alone. I know that the only 2 people that really know what took place in that relationship are the 2 people that were in it. There's always 2 sides to the story of a marriage breakdown. Its not my place to do anything but support him. The issues he has with his ex, he can take care of on his own...and vice versa.
He's got great kids...and you don't have great kids without great parents. Therefore, I respect the job his ex-wife did as a mother and would never try to make her uncomfortable or disrespect her.
I hear a lot of stories about new gfs or new wives ranting and raving about their new partners' ex. My advice...let them deal with their own past relationship and stay out of it except to provide support. I think it makes the transition for everyone easier...especially the kids.