  A general class of weighted multilinear Hardy-Ces\`aro operators that acts on
the product of Lebesgue spaces and central Morrey spaces. Their sharp bounds
are also obtained. In addition, we obtain sufficient and necessary conditions
on weight functions so that the commutators of these weighted multilinear
Hardy-Ces\`aro operators (with symbols in central BMO space) are bounded on the
product of central Morrey spaces. These results extends known results on
multilinear Hardy operators.
