Do leaves grow larger by adding cells at the centre or at the edge?
Plant leaves develop from leaf primordium or meristem tissue (this tissue has special properties that allow it to continue dividing to make more more cells, i.e. stem cells - not stem cells like cells in the stem but the technical term 'stem cells). Because of the hormone balances to maintain this division property the meristem tissue will remain close to the stem or branch of the plant at the base of the leaf whilst the new cells added to the leaf slowly move outwards.
https://www.sciencedirect.com/science/article/pii/S1369526616300929