As James said the individual units do not get broken down to fit in multiple ships.  Each troop transport bay has a capacity of 5, each small troop transport bay has a capacity of 1.  A company is 1 point, a battalion is 5, a brigade is 25, however a brigade of combat troops can be broken down into different ships due to there being more than 1 unit involved.  The real pain comes about if you try to transport the low tech infantry/armor divisions which are equal to two brigades (50 points)  For that you will need 1 ship with 10 troop transport bays. 

This also holds true when loading units into the combat drop modules.  So be carefull about putting the small drop modules on your main assault ships as they will not be able to drop anything but marine compaines.  You can have 5 companies use a single troop transport bay or drop module however.

Hope this helps
Brian

I'm trying to load an engineer brigade onto my fleet which consists of 5 troop transports, each of which has a capacity of "1 batallion."  I thought this should be just enough, but I'm getting an "insufficient space" message.

How many of these ships do I need?