Prepositions: the difference between 'into/in to' and 'onto/on to'

I've recently been asked about why these prepositions are sometimes written as one word and other times are separated.

In, into, on and onto are all prepositions.  We usually use 'in' and 'on' to give information about position of the subject in relation to something else.  For example:

• He splashed in the puddles.
• She stood on the wall.

The prepositions 'into' and 'onto' are usually used to indicate direction, movement or transformation:

• He raced into the lead.
• She climbed onto the wall. 
• She turned him into a frog.

Sometimes either preposition can be used grammatically in a sentence.  However, consider the difference in meaning in the following sentences:

• The boy jumped in the pool.
• The boy jumped into the pool. 

Although both constructions are possible, there is a subtle difference between them.  In the first, the boy is in the pool and jumping around; in the second, he starts out of the pool and the direction of the jump means he ends up in the pool.  It is the semantics which must be considered when deciding which preposition to use.

A further complication arises when the verb in a sentence is a phrasal or prepositional verb.  Many verbs are constructed by using a verb and a preposition: hand in, turn in, give in, build on, rely on, etc.  When these are followed by 'to', we really need to think about the sense we are creating for the reader.  Joining the final preposition of the verb phrase to what follows may change the meaning altogether if care is not taken.  Consider the following sentences:

• My homework should be handed in to my teacher by Thursday.
• My homework should be handed into my teacher by Thursday.  (Not possible - the adverbial phrase 'to my teacher' cannot be joined to the 'in'.)

• We need to turn ourselves in to the police. 
• We need to turn ourselves into the police. 

• I'll give in to keep the peace.  (Correct as the 'to' starts an infinitive verb structure and non-finite clause)
• I'll give into keep the peace.  (Not possible)

• Her success can be built on to ensure her future. (Correct - the non-finite clause 'to ensure her future' has to be separate.)
• Her success can be built onto ensure her future.  (Not possible)

• His father could be relied on to keep him safe. (Correct - the non-finite clause must be separate.)
• His father could be relied onto keep him safe. (Not possible).

We can see from the above examples that we have to consider firstly whether the 'to' that follows the verb is acting as a preposition or the start of an infinitive verb structure.  Once we have decided that the 'to' is acting as a preposition, we need to consider whether we want to indicate direction, movement or transformation.  If so, then 'into' or 'onto' will be appropriate prepositions to use.