[DanBC]

If you're inside the catchment area it's very difficult for the GP to not register you. GPs are expected to provide service to almost anyone living in their region.

If you're outside the catchment area the GP can chose to offer full service; offer limited service; or offer no service.

The full service includes things like home visits, so it's not surprising that GPs seek to limit that to patients who live far away.

For people who are travelling there are temporary registrations, but also GP walk in centres and GP out-of-hours services.