Hi Gaz,
As your transponder is pumping out power on 1090MHz, this will have the most significant effect at close range on the ADSB side of PAW (same frequency). Effects can range from desensitising the receiver - effectively blocking reception of other aircraft (though this is 'unlikely' as transponder transmissions are short pulses rather than continuous transmissions) to at
very close range, potentially damaging the receiver. These effects are normally easily avoided by antenna separation.
Due to the frequency difference, the effect on the P3i side will be far less significant, though again at
very close range, some desensitisation might still occur, so best to keep them apart, preferably by at least one 'wavelength' - somewhere about 275mm minimum in theory (rough calculation before the pedants get on my case) though generally the more distance between transmitting and receiving antennas the better. You have to balance this against increasing losses in longer lengths of coax cable, however.
The most important point to consider is clear view of approaching traffic - especially for the P3i antenna as this is working on much lower power levels than the 1090MHz side. If you haven't already done so, please read the documents on Permanent Installation and Antenna placement on the PAW website
www.pilotaware.com I got round the issue by fitting my transponder and antenna underneath and towards the rear of my (flexwing) aircraft with the other antennas at the front. Just to complicate matters I also run FLARM In/Out and sometimes also other test equipment on adjacent frequencies, but all generally get along fine, so don't get too hung up on it - just try to keep the 'low power / receive stuff' as far as practicable from your Transponder/ADSB transmit antenna and everything should be OK.
Regards
Peter