pic=Plot3D[x^2+y^2,{x,-1,1},{y,-1,1},BoxRatios->{2*Sqrt[2],2*Sqrt[2],2},PlotRangePadding->{Sqrt[2]-1,Sqrt[2]-1,0},Boxed->False,Mesh->20,AxesLabel->{"X","Y","Z"},ViewPoint->{1.3,-2.4,1}]

Export["elliptic_paraboloid_square_domain.png",pic,ImageSize->300]