first up, as you may have seen, i've had trouble with sizes of hoses an my header tank, and the hoses. both are 16mm, but they rattle when slid on each other.
assuming the hose is actually 17mm, but listed as 16mm, will a 13mm hose stretch over the pipe on the tank?

and is 13mm too small for connecting up the tank to the bottom hose? i shouldn't think so, as the tank only has 8mm and 6mm hose going into the top of it... 14mm total

don't like problems with hoses... but think i've got this one sorted now lol

The standard automotive hoses bore sizes are a carry over from inch sizes 1/2" and 5/8".
A 1/2" hose won't stretch to 5/8" without braking the reinforcing fibres.
If you are using silicone hoses u may have more success using rubber hose.
It is also possible the hose required by the header is special size - ie 1/2" bore hose with a specially expanded end.

13mm wont stretch over 17mm.

lol i don't want to stretch it over 17mm

the hose i had was listed as 16mm, its printed on the hose too. the tank connection is bang on 16mm, but they don't fit tight. if you push it on it doesn't hold at all.
i think i've got a plan though... lol if it doesn't work, i'll try rubber as BT suggested

taken a careful measurement of the '16mm hose' and the i.d. is in fact 17mm...
guess i have to order 1 or 2mm smaller where i can then...