I think it's likely that if the UK ever got rid of their monarchy, basically every other EU country would follow shortly after in the next 2-5 years.
Similarly, I think if Sweden of The Netherlands or some non-Spain country abolished the monarchy then almost every other country except the UK would follow.
Spain probably wouldn't cause too much of a tidal wave though, as it's own monarchy is too much of a historical anomaly.
This seems far fetched. Britain is not a role model for countries in continental Europe and the monarchy is a matter of national tradition, not something influenced by what other countries do,
I suppose the Scandinavian countries might nfluence each other somewhat, since we use each other as points of reference, but apart from that why for instance should Danes care if the monarchy is abolished in Belgium?
I honestly don't see Denmark being effected by Sweden or vice versa (at least no more than any other country abolishing the monarchy), I think or public debate and media have become too alien to each other for us to see such a effect. You can see it right now, where Sweden have strong anti-monarchism media, while in Denmark it doesn't fill anything in the general debate.
Abolishing the monarchy in Norway on the other hand could have some effects, while we may look down on the Norwegians (as lovable hillbillies), we are often inspired by them.