Migration properties at different restart times and therefore for a different gap shape. Left: temporal evolution of the semi-major axis a_p (solid lines) and radial position (shaded areas) of the planet. Whatever the initial condition, the planet migration is eventually slow and outward for β₀ = 10³ once the gap has been carved. Right: temporal evolution of the planet eccentricity e_p, initially small (<1.5%) before increasing abruptly (≃7%) for the cases ℳ₂₀₀ and ℳ₃₀₀.