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Let the star on $n$ vertices, namely $K_{1,n-1}$ be denoted by $S_n$. Ifevery two coloring of the edges of a complete balanced multipartite graph $K_{j\times s}$ there is a copy of $S_n$ in the first color or a copy of $S_m$ inthe second color, then we will say $K_{j \times s}\rightarrow (S_n,S_m)$. Thesize Ramsey multipartite number $m_j(S_n, S_m)$ is the smallest natural number$s$ such that $K_{j \times s}\rightarrow (S_n,S_m)$. In this paper, we obtainthe exact values of the size Ramsey numbers $m_j(S_n,S_m)$ for $n,m \ge 3$ and$j \ge 3$.

Diagonal Ramsey numbers in multipartite graphs related to stars