What determines the size and shape of cells in multicellular organisms?

the same thing that limits the size of cells in all organisms: the surface area to volume ratio.

Cells are independent units, and to function require diffusion of nutrients across the cell membrane to the mitochondria. As a cell increases in size, it requires more energy for this operation to take place, while the volume of the cell increases at a rate that exceeds that of the SA. Thus, as the cell increases in size, it becomes increasingly unstable (physically) and requires more energy.

hope this helps. :)

If you mean developmentally, it has to do with the chemicals that surround that cell when it is growing. Those chemicals are a function of the cell types around it, so it is a bit of a cyclical process.