Escape velocity is dependent on mass of the planet or star you are trying to escape from and the current distance from the center of the planet or star.

I am pretty sure it is also dependent on the direction of the motion. I think the velocity component parallel to a radius vector must be equal to escape velocity. I am not certain of this, but it seems reasonable.

The mass of the escaping object affects the force or energy required to achieve escape velocity, but the escape velocity is not dependent on this mass.