My son and his baby's mom were never married but are living together, the baby is almost 2 years old. There is constant fighting in the home and my son wants to move out of state to get away and get on his feet to better take care of his son. How does he accomplish this without getting abandonment charges against him ? Thank you

Is he on the birth certificate?
Are there court orders of any kind?
What state are they in now?
Did you read the posts on Abandonment at the top of the page?

As indicated, moving out is not "abandonment" in most states. To avoid being sued for child support, he should get a court order (or child support agency determination) specifying how much he needs to pay for child support, and then pay CS through the court or agency (if possible in his jurisdiction).

He just leaves. The rest is worked out through the courts, but abandonment is not something she can even sue him for.

First any question on law needs to include your general locale as laws vary by area. Abandonment is a criminal charge which stems from leaving a child without adult supervision. That is not the case here, so there are unlikely to be abandonment charges filed against him. However, he will still be required to support the child. If he does not, he may face criminal charges in a very few states.

Since they aren't married he can't be charged with abandoning the mother either in civil or criminal courts.

But, rather than run away from the situation he should man up and go to court to establish a child support payment and visitation agreement.

... Abandonment is a criminal charge which stems from leaving a child without adult supervision. That is not the case here, so there are unlikely to be abandonment charges filed against him. However, he will still be required to support the child. If he does not, he may face criminal charges in a very few states.

Since they aren't married he can't be charged with abandoning the mother either in civil or criminal courts. ... .

"Abandonment" as a criminal charge meaning failure to support one's children (as opposed to "leaving a child without adult supervision" is only used in a very few states (Georgia, I believe, and possibly one or two others). Criminal charges (or contempt, which has certain similarities) for non-support is used in a large number of states, I believe.

I don't know of any state where failure to support the mother of one's child is a crime. Child support is for the child, but normally payable to the custodial parent (such as a mother). Spousal support (or alimony) is awarded sometimes in most states, but failure to pay it is a civil, not criminal matter.

Agreed, if this is America, he says goodbye and leaves. He should file in court for visitation and have a court order child support amount arranged. But he just leaves and makes sure he pays child support.

... But he just ... makes sure he pays child support.

The important thing is that he makes sure he documents his CS payments. It would be best that a CS order (setting a specific monthly amount) is in place, but at the very least he should keep copies of checks (never cash, etc.) he sends her. Each check should specify that it is child support, so that she can't later claim it was a gift or something.