dd2 (2.5) won the parcel the other day and won a vile rubbery ball thing with spikes that you can stretch - my goodness does she love it, she was the ENVY of the party. So I can highly recommend those, they look HORRIBLE.
I just packed up a forfeits pass the parcel for saturday's party....too many children coming to do a prize every layer so "lucky" winners get to hop across the circle, sing a nursery rhyme etc.
Howver they are 4 and 6 so perhaps a bit hard for 3yo.
Prize in the middle is some playmobil, but for younger children I have done a little box of jigsaws (from Asda) or a book (from my stash of cheapies from The Red House) or colouring pencils always good.