What are the laws about child abandoment?

Section 211.447.4(1)(b) RSMo. 2000 finds a child is abandoned "if, for a period of six months or longer... [t]he parent has, without good cause, left the child without any provision for parental support and without making arrangements to visit or communicate with the child, although able to do so... "
"Abandonment is defined as the voluntary and intentional relinquishment of custody of a child with the intention that the severance be of a permanent nature or as the intentional withholding by a parent of his care, love, protection and presence without just cause or excuse. "

According to Section 211.447.6, incarceration alone is not grounds to terminate a person's parental rights, but incarceration does not exempt a parent from their obligations to their child

Not exactly sure what you are looking for.