if you need to join the new plastic guttering to your neighbours existing cast iron guttering then it depends on what part your neighbours guttering is.
if its an internal or external joint, ie did the one you take off leave your neighbour with a socket which your guttering went into?
if it did then position your new plastic guttering into the socket, screw through the existing cast and the new plastic putting a self tapper screw and use a good sealant, DONT USE the cheap roof and gutter sealants there rubbish and depend also on the joint being bone dry, the chances of a bone dry joint are quite franckly 1 in 100, they also depend on the joint being free from rust,dust ect so give them a miss and get a good sealant like aquaseal or leadmate.
if its an internal end you have left then use a union between the new plastic and the neightour and seal as appropiate.
there is never a sure fire way of sealing any non matching guttering whenever its 2 plastic or 1plastic/1 cast, or asbestos ect.just have to use common sense.
if its square guttering your putting up and your neigbour has round, then you can get a connector for this that works great.there is a style that has clasps and a bolt which you tighten to fit, but there is a much better sq/end union from everwhite that in 90% of cases works perfect.brent martin do the clip and bolt style which is 3 times as expensive and not such a good finish these can be used also when the neighbour has round cast and you want square plastic.
truly the worst guttering joint to do is new plastic square or round onto a cast iron ogee style the only half decent solution for this style is to heat the end of the new plastic and soften it to try to shape as best you can into the ogee shape.this type is m,ainly found on edwardian and victorian houses.
