After various failures with cheap potties, we ended up with the chair-style potties from M&S (Thomas design). They are now 17 quid each and the design has changed slightly (luckily a friend was selling hers 2nd hand so I didn't pay that).
Seb is still using them some of the time (at 3.5) - partly because he can't reach the lightswitch in our downstairs loo but the potty is in the kitchen, but mostly because he likes them and won't be persuaded to use the toilet (although he copes fine out and about without a potty).
We don't generally get wee everywhere, except when he sits there too long and the lift-out tray bit sticks to his bum so it spills as he stands up.
They are not small though.
Ros