The structure and collapse of linear three-dimensional magnetic neutral points is studied by varying the four parameters (p, q,j|,j) that define, in general, the linear field of a neutral point. The effect of these parameters on both the skeleton structure (i.e. the fan and spine) and the actual field line structure of the null is considered. It is found that one current component (j) causes the skeleton structure of the null to fold up from its potential state, whereas the other current component (j|;) causes the field lines to bend. The two other parameters (p,q) determine the potential structure of the null and cause the null to transform from a three-dimensional null to a two-dimensional null and from a positive (type B) null to a negative (type A) null. To investigate the collapse of three-dimensional nulls, solutions to the linear, low-beta ideal magnetohydrodynamic equations are found. It is found that three-dimensional null points can collapse if the field line foot-points are free and energy can propagate into the system.