  The problem of determining the optimal minimum degree condition for a
balanced bipartite graph on 2ms vertices to contain m vertex disjoint copies of
K_{s,s} was solved by Zhao. Later Hladk\'y and Schacht, and Czygrinow and
DeBiasio determined the optimal minimum degree condition for a balanced
bipartite graph on 2m(s+t) vertices to contain m vertex disjoint copies of
K_{s,t} for fixed positive integers s<t.
  For a balanced bipartite graph G[U,V], let \delta_U be the minimum degree
over all vertices in U and \delta_V be the minimum degree over all vertices in
V. 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 show
that the optimal value depends on D:=|\delta_V-\delta_U|. When D is small, we
show 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 than
n+2s-2s^{1/2}. However, when D=n-C for some constant C, we show that there
exist graphs with \delta_U+\delta_V\geq n+s^{s^{1/3}} which cannot be tiled
with K_{s,s}.
