The 11+ is a competitive exam and can be set by the LS (stte only), an individual school or group of schools, or by a separate provider (like ISEB and the CE exam board). The usually cover maths, English, verbal reasoning and non-verbal reasoning. Ties are generally broken by consideration of distance (nearer having priority) or by lottery.
Common entrance exams are used by the private sector only, and is not competitive (ISEB 13+). Students must have a conditional offer from the school in order to sit the test. These conditional offers are usually made on the basis of a pretest in year 6 or 7, by interview, by reference, or on a first-come first-served basis – sometimes a combination of these. The papers are set by ISEB but the school marks them. If the candidate achieves a passing grade, he or she will be admitted to the school.
There may also be 13+ scholarship exams to determine additional funding, or the school may provide its own exam for this purpose. These are usually competitive, for obvious reasons.