When I was small, if I was sick the doctor (GP) would often visit us at home. I remember this with fond memories. Now and over the last 25 years home visits are a premium, rare. It is seldom that they visit at home. It is much harder to have a longer term relationship as the doctors move around a lot, however it is still sometimes possible to see the same doctors for many years. These days you are not assigned a particular doctor, you are part of the medical practice or surgery and will most often see any doctor on duty or a locum doctor. There is now so much pressure because more people come to the doctor than in the past, as the older generations often stayed at home and did not always seek help for little things. The plus of this is that those who stayed at home in the past now feel able to come and visit the doctor, because even little things can be important and may be more of a problem than they realised. There are several other reasons for the changes though, for instance there are more people to care for than in the past. However, I am happy that we have health care, so it is not a complaint.

Really depends on health coverage in most cases. The only times my family or I maintained any sort of long-term relationship with our doctor is when it was a Family/General Practitioner (someone who does generally everything, not necessarily a specialist in any field) within an HMO (a plan that constitutes a fixed group of doctors that accept that particular insurance).

Usually you have a Primary Physician established early on, and they hold on to your charts and records. Your primary physician being someone close by, and someone you trust (possibly other friends go to the same doctor). Trust is really the only binding aspect here, and doctors you frequent will at least be more knowledgeable about any health conditions you may have.

It's not possible in Colombia. Health insurance companies are all the time changing physicians.