Yes, space is a limiting factor for the plant population.
The space occupied by the plant on the earth determines the amount of the nutrition derived from the soil, if the land is occupied by many plants, the space for the adherence and the nutrient intake would be a factor for competition.
All the plants need sunlight to survive, as it is the source of energy for them. In case, a tree or a plant occupies a huge aerial space, then it would shade the sunlight for the smaller plants, hence, the plants cannot grow in completely shaded region.