I didn't think culture actualy continued to spread.
Well, it does but there are practical limits.
The distance that culture will spread is limited by several factors including population (both friendly / opposing), distance (each "hop" has a flat reduction), tech levels (both sides), opposing broadcast centers, number of cap ships in area, etc.
In a simple example, 2 planets adjacent to each other and identical (population, tech, etc) the culture line will eventually end up half way down the phase lane to each other. Cap ships reject opposing culture so just parking a friendly cap ship will start "pushing back" the opposing influence.