The spatial distribution of plasma density and the transition power for capacitive (E) to inductive (H) mode transition are studied in planar type inductively coupled plasmas with different antenna sizes. The spatial plasma distribution has a relatively flat profile at a low gas pressure, while the plasma profile is affected by the antenna size at higher gas pressure. The transition power for the E to H mode transition is shown to be critically affected by the antenna size. When the discharge is sustained by a small one-turn antenna coil, the transition power has a minimum value at Ar gas of 20 mTorr. However, the minimum transition power is shown at a relatively high gas pressure (40-60 mTorr) in the case of a large one-turn antenna coil. This change in the transition power can be understood by the thermal transport of the energetic electrons with non-local kinetics to the chamber wall. This non-local kinetic effect indicates that the transition power can also increase even for a small antenna if the antenna is placed near the wall.