my 2006 525xi sputters when you accelerate, but stops when you let off the gas

What is your question?

The coils and plugs have been replaced as well as a cable that connects at the battery that has a chip that controls, heater, and a few other items.

What makes this problem better or worse?

it seems to be worse after heating up

How long has your 2006 BMW 525xi had this problem?

about a year