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The problem of determining the optimal minimum degree condition for abalanced bipartite graph on 2ms vertices to contain m vertex disjoint copies ofK_{s,s} was solved by Zhao. Later Hladk\'y and Schacht, and Czygrinow andDeBiasio determined the optimal minimum degree condition for a balancedbipartite graph on 2m(s+t) vertices to contain m vertex disjoint copies ofK_{s,t} for fixed positive integers s<t.  For a balanced bipartite graph G[U,V], let \delta_U be the minimum degreeover all vertices in U and \delta_V be the minimum degree over all vertices inV. We consider the problem of determining the optimal value of\delta_U+\delta_V which guarantees that G can be tiled with K_{s,s}. We showthat the optimal value depends on D:=|\delta_V-\delta_U|. When D is small, weshow that \delta_U+\delta_V\geq n+3s-5 is best possible. As D becomes larger,we show that \delta_U+\delta_V can be made smaller, but no smaller thann+2s-2s^{1/2}. However, when D=n-C for some constant C, we show that thereexist graphs with \delta_U+\delta_V\geq n+s^{s^{1/3}} which cannot be tiledwith K_{s,s}.

Tiling in bipartite graphs with asymmetric minimum degrees