When I should use one to one relationship?
1 to 0..1
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The "1 to 0..1" between super and sub-classes is used as a part of "all classes in separate tables" strategy for implementing inheritance.
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A "1 to 0..1" can be represented in a single table with "0..1" portion covered by NULL-able fields. However, if the relationship is mostly "1 to 0" with only a few "1 to 1" rows, splitting-off the "0..1" portion into a separate table might save some storage (and cache performance) benefits. Some databases are thriftier at storing NULLs than others, so a "cut-off point" where this strategy becomes viable can vary considerably.
1 to 1
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The real "1 to 1" vertically partitions the data, which may have implications for caching. Databases typically implement caches at the page level, not at the level of individual fields, so even if you select only a few fields from a row, typically the whole page that row belongs to will be cached. If a row is very wide and the selected fields relatively narrow, you'll end-up caching a lot of information you don't actually need. In a situation like that, it may be useful to vertically partition the data, so only the narrower, more frequently used portion or rows gets cached, so more of them can fit into the cache, making the cache effectively "larger".
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Another use of vertical partitioning is to change the locking behavior: databases typically cannot lock at the level of individual fields, only the whole rows. By splitting the row, you are allowing a lock to take place on only one of its halfs.
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Triggers are also typically table-specific. While you can theoretically have just one table and have the trigger ignore the "wrong half" of the row, some databases may impose additional limits on what a trigger can and cannot do that could make this impractical. For example, Oracle doesn't let you modify the mutating table - by having separate tables, only one of them may be mutating so you can still modify the other one from your trigger.
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Separate tables may allow more granular security.
These considerations are irrelevant in most cases, so in most cases you should consider merging the "1 to 1" tables into a single table.
See also: Why use a 1-to-1 relationship in database design?
My 2 cents.
I work in a place where we all develop in a large application, and everything is a module. For example, we have a users table, and we have a module that adds facebook details for a user, another module that adds twitter details to a user. We could decide to unplug one of those modules and remove all its functionality from our application. In this case, every module adds their own table with 1:1 relationships to the global users table, like this:
create table users ( id int primary key, ...);
create table users_fbdata ( id int primary key, ..., constraint users foreighn key ...)
create table users_twdata ( id int primary key, ..., constraint users foreighn key ...)
If you place two one-to-one tables in one, its likely you'll have semantics issue. For example, if every device has one remote controller, it doesn't sound quite good to place the device and the remote controller with their bunch of characteristics in one table. You might even have to spend time figuring out if a certain attribute belongs to the device or the remote controller.
There might be cases, when half of your columns will stay empty for a long while, or will not ever be filled in. For example, a car could have one trailer with a bunch of characteristics, or might have none. So you'll have lots of unused attributes.
If your table has 20 attributes, and only 4 of them are used occasionally, it makes sense to break the table into 2 tables for performance issues.
In such cases it isn't good to have everything in one table. Besides, it isn't easy to deal with a table that has 45 columns!
If data in one table is related to, but does not 'belong' to the entity described by the other, then that's a candidate to keep it separate.
This could provide advantages in future, if the separate data needs to be related to some other entity, also.